CALCULATION OF AREA, SURFACE AREA AND VOLUME

Aptitude and Reasoning Course 

Volume 

Area, Surface area and 

CALCULATION OF AREA, 

SURFACE AREA AND VOLUME 

SITAMS, Chittoor Page 1


Volume 


A. Module Objective 

This Module describes various standard geometrical structures that exist and 

methods/formulas for calculating its characteristic values that can be used for various 

applications/calculations. The structures include circle, triangle, cylinder etc., that exists with 

in or as a shape, in all the practical entities we see in our daily life. So, calculating its area, 

Volume and perimeter gives the mathematical insight about the structure. 

For example, in order to determine the number of tiles of specific shape to be placed 

over the floor of specific dimension, area of both tile and the floor become the basis. 

B. Prerequisites (Related Formulas):- 

1. Area Calculations: Area is a quantity that expresses the extent of a twodimensional 

surface or shape in the plane. Area can be understood as the amount of 

material with a given thickness that would be necessary to fashion a model of the 

shape, or the amount of paint necessary to cover the surface with a single coat. 

1 square kilometer = 1,000,000 square meters, 

1 square meter = 10,000 square centimetres = 1,000,000 square millimeters 

1 square centimetre = 100 square millimeters 

1 square yard = 9 square feet 

1 square mile = 3,097,600 square yards = 27,878,400 square feet 

a. square = a 2 

b. rectangle = ab 

c. parallelogram = bh 

d. trapezoid = h/2 (b 1 + b 2 ) 

e. circle = pi r 2 

f. ellipse = pi r 1 r 2 



Volume 


g. triangle = 

h. equilateral triangle 

i. triangle given a,b,c = [s(s-a)(s-b)(s-c)] where 

s = (a+b+c)/2 (Heron's formula) 

j. isosceles triangle = (b/4)*(√(4a 2 -b 2 )) 

k. regular hexagon = (3√3/2)*a 2 where a is its side 

l. rhombus = 0.5*diagonal 1 * diagonal 2 

m. 

2. Volume Calculations: Volume is the quantity of threedimensional 

space enclosed by some closed boundary, for example, the space that 

a substance (solid, liquid, gas, or plasma) or shape occupies or contains. [1] Volume 

is often quantified numerically using the SI derived unit, the cubic metre. 

1 litre = (10 cm) 3 = 1000 cubic centimetres = 0.001 cubic metres, 

1 cubic metre = 1000 litres. 

Small amounts of liquid are often measured in millilitres, 

where 1 millilitre = 0.001 litres = 1 cubic centimetre. 

a. cube = a 3 

b. rectangular prism = a b c 

c. irregular prism = b h 

d. cylinder = b h = pi r 2 h 

e. pyramid = (1/3) b h 



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f. cone = (1/3) b h = 1/3 pi r 2 h 

g. sphere = (4/3) pi r 3 

h. ellipsoid = (4/3) pi r 1 r 2 r 3 

3. Surface Area Calculations: Surface area is the measure of how much exposed 

area a solid object has, expressed in square units. Mathematical description of the 

surface area is considerably more involved than the definition of arc length of a 

curve. 

a. Surface Area of a Cube = 6 a 2 (a is the length of the side of 

each edge of the cube). 

In words, the surface area of a cube is the area of the six squares that 

cover it. The area of one of them is a*a, or a 2 . Since these are all the same, 

you can multiply one of them by six, so the surface area of a cube is 6 times 

one of the sides squared. 

b. Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac 

(a, b, and c are the lengths of the 3 sides). 

In words, the surface area of a rectangular prism is the area of the six 

rectangles that cover it. But we don't have to figure out all six because we know 

that the top and bottom are the same, the front and back are the same, and the left 

and right sides are the same. 

The area of the top and bottom (side lengths a and c) = a*c. Since there are 

two of them, you get 2ac. The front and back have side lengths of b and c. The 

area of one of them is b*c, and there are two of them, so the surface area of those 

two is 2bc. The left and right side have side lengths of a and b, so the surface area 

of one of them is a*b. Again, there are two of them, so their combined surface 

area is 2ab. 

c. Surface Area of Any Prism (b is the shape of the ends) 

Surface Area = Lateral area + Area of two ends 

(Lateral area) = (perimeter of shape b) * L 



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Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b) 

d. Surface Area of a Sphere = 4 pi r 2 (r is radius of circle) 

e. Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h (h is the height 

of the cylinder, r is the radius of the top) 

Surface Area = Areas of top and bottom +Area of the side 

Surface Area = 2(Area of top) + (perimeter of top)* height 

Surface Area = 2(pi r 2 ) + (2 pi r)* h 

In words, the easiest way is to think of a can. The surface area is the areas of 

all the parts needed to cover the can. That's the top, the bottom, and the paper 

label that wraps around the middle. You can find the area of the top (or the 

bottom). That's the formula for area of a circle (pi r 2 ). 

Since there is both a top and a bottom, that gets multiplied by two. The side is 

like the label of the can. If you peel it off and lay it flat it will be a rectangle. The 

area of a rectangle is the product of the two sides. One side is the height of the 

can, the other side is the perimeter of the circle, since the label wraps once around 

the can. 

So the area of the rectangle is (2 pi r)* h. Add those two parts together and you 

have the formula for the surface area of a cylinder. 

4. Perimeter Calculations: A perimeter is a path that surrounds an area. The word 

comes from the Greek peri (around) and meter (measure). The term may be used 

either for the path or its length - it can be thought of as the length of the outline of 

a shape. 

a. square = 4a 

b. rectangle = 2a + 2b 

c. triangle = a + b + c 

d. circle = 2pi r 

circle = pi d (where d is the diameter). The perimeter of a circle is more 

commonly known as the circumference. 



Volume 


Properties of various Geometrical structures: 

a. Triangle 

In an equilateral triangle all sides have the same length. An equilateral triangle is also 

a regular polygon with all angles measuring 60°. 

In an isosceles triangle, two sides are equal in length. An isosceles triangle also has 

two angles of the same measure; namely, the angles opposite to the two sides of the same 

length; this fact is the content of the Isosceles triangle theorem. 

In a scalene triangle, all sides are unequal. The three angles are also all different in 

measure. Some (but not all) scalene triangles are also right triangles. 

A right triangle (or right-angled triangle, formerly called a rectangled triangle) has 

one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is 

the hypotenuse; it is the longest side of the right triangle. The other two sides are called 

the legs of the triangle. 

Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of 

the two legs is equal to the square of the length of the hypotenuse: a 2 + b 2 = c 2 , 

where a and b are the lengths of the legs and c is the length of the hypotenuse. 

Triangles that do not have an angle that measures 90° are called oblique triangles. 

A triangle that has all interior angles measuring less than 90° is an acute 

triangle or acute-angled triangle. 

A triangle that has one angle that measures more than 90° is an obtuse 

triangle or obtuse-angled triangle. 

A "triangle" with an interior angle of 180° (and collinear vertices) is degenerate. 

b. Quadrilateral 

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or 'edges') 

and four vertices or corners. Sometimes, the term quadrangle is used, by analogy 

with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6- 

sided) and so on. The word quadrilateral is made of the wordsquad (meaning "four") 

and lateral (meaning "of sides"). 

The diagonals of parallelogram bisect each other 

Each diagonal of a parallelogram divides it into two triangles of the same area 

The diagonals of rectangle are equal and bisect each other 



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The diagonals of square are equal and bisect each other at right angles 

The diagonals of rhombus are unequal and bisect each other at right angles 

c. Circle 

The circle is the shape with the largest area for a given length of perimeter. 

A circle's circumference and radius are proportional. 

The area enclosed and the square of its radius are proportional. 

The constants of proportionality are 2π and π, respectively. 

The circle which is centered at the origin with radius 1 is called the unit circle. 

Some Important Metrics: 

1. 10,000 sq meters = 1 hectare 

2. 100 hectares = 1 sq kilo meter 

3. 1000 millimeters = 1 meter 

4. 100 centimeters = 1 meter 

5. 1000 metres = 1 kilometer 

6. 1000 kilograms = 1 mega gram or 1 tonne 

7. 3.6 kilometers per hour = 1 meter per second 

8. 3600 kilometers per hour = 1 kilometer per second 

C. Solved Examples 

1. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling 

along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, 

then the area of the park (in sq. m) is: 

A.15360 B.153600 

C.30720 D.307200 

Answer & Explanation 

Answer: Option B 

Explanation: 

Perimeter = Distance covered in 8 min. = 12000 x 8 

60 m = 1600 m. 

Let length = 3x metres and breadth = 2x metres. 



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Then, 2(3x + 2x) = 1600 or x = 160. 

Length = 480 m and Breadth = 320 m. 

Area = (480 x 320) m 2 = 153600 m 2 . 

2. An error 2% in excess is made while measuring the side of a square. The percentage of 

error in the calculated area of the square is: 

A.2% 

C.4% 

B.2.02% 

D.4.04% 


Answer: Option D 

Explanation: 

100 cm is read as 102 cm. 

A 1 = (100 x 100) cm 2 and A 2 (102 x 102) cm 2 . 

(A 2 - A 1 ) = [(102) 2 - (100) 2 ] 

= (102 + 100) x (102 - 100) 

= 404 cm 2 . 

404 

Percentage error = x 100 = 4.04% 

100 x 100 % 

3. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the 

rectangle is 216 sq. cm, what is the length of the rectangle? 

A.16 cm B.18 cm 

C.24 cm D.Data inadequate 

E.None of these 



Explanation: 

2(l + b) = 

5 

b 1 

2l + 2b = 5b 

3b = 2l 



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b = 2 l 

3 

Then, Area = 216 cm 2 

l x b = 216 

l x 2 l= 216 

3 

l 2 = 324 

l = 18 cm. 

4. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% 

is: 

A.40% 

C.44% 

B.42% 

D.46% 


Answer: Option C 

Explanation: 

Let original length = x metres and original breadth = y metres. 

Original area = (xy) m 2 . 

New length = 120 x = 6 x 

100 m 5 m. 

New breadth = 120 y = 6 y 

100 m 5 m. 

New Area = 6 x x 6 y m 

2 = 36 xy 

5 5 25 m 2 . 

The difference between the original area = xy and new-area 36/25 xy is 

= (36/25)xy - xy 

= xy(36/25 - 1) 

= xy(11/25) or (11/25)xy 

xy 

Increase % = 11 

x 1 x 100 = 44%. 

% 

5. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the 



Volume 


middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 

2109 sq. m, then what is the width of the road? 

A.2.91 m 

B.3 m 

C.5.82 m 

D.None of these 



Explanation: 

Area of the park = (60 x 40) m 2 = 2400 m 2 . 

Area of the lawn = 2109 m 2 . 

Area of the crossroads = (2400 - 2109) m 2 = 291 m 2 . 

Let the width of the road be x metres. Then, 

60x + 40x - x 2 = 291 

x 2 - 100x + 291 = 0 

(x - 97)(x - 3) = 0 

x = 3. 

6. The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet 

is 4 

feet. What is the area of the closet in square feet? 

A.5 1 B.13 1 4 

2 

C.27 D.37 



Explanation: 

Other side= 15 2- 9 2ft 

2 2 

= 225 - 81 ft 

4 4 

= 144 ft 

4 

=6 ft. 

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft. 



Volume 


7. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. 

The percentage of decrease in area is: 

A.10% 

C.20% 

B.10.08% 

D.28% 



Explanation: 

Let original length = x and original breadth = y. 

Decrease in area= xy - 

= xy - 18 xy 

25 

80 xx 

90 y 

100 100 

= 7 xy. 

25 

7 1 

Decrease % = xy x x 100 = 28%. 

25 xy % 

8. A man walked diagonally across a square lot. Approximately, what was the 

percent saved by not walking along the edges? 



Explanation: 

Let the side of the square(ABCD) be x metres. 

Then, AB + BC = 2x metres. 

AC = 2x = (1.41x) m. 

Saving on 2x metres = (0.59x) m. 



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Saving % = 0.59xx 100 % 

= 30% (approx.) 

9. The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the 

rectangle must be: 

A.9 cm B.18 cm 

C.20 cm D.41 cm 



Explanation: 

l 2 + b 2 = 41. 

Also, lb = 20. 

(l + b) 2 = (l 2 + b 2 ) + 2lb = 41 + 40 = 81 

(l + b) = 9. 

Perimeter = 2(l + b) = 18 cm. 

10. What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm 

long and 9 m 2 cm broad? 

A.814 B.820 

C.840 D.844 


Answer: Option A 

Explanation: 

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. 

Area of each tile = (41 x 41) cm 2 . 

Required number of tiles = 1517 x 902 = 814. 

41 x 41 

11. The difference between the length and breadth of a rectangle is 23 m. If its perimeter 

is 206 m, then its area is: 

A.1520 m 2 B.2420 m 2 

C.2480 m 2 D.2520 m 2 




Volume 



Explanation: 

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. 

Solving the two equations, we get: l = 63 and b = 40. 

Area = (l x b) = (63 x 40) m 2 = 2520 m 2 . 

12. The length of a rectangle is halved, while its breadth is tripled. What is the percentage 

change in area? 

A.25% increase 

C.50% decrease 

B.50% increase 

D.75% decrease 



Explanation: 

Let original length = x and original breadth = y. 

Original area = xy. 

New length = x . 

2 

New breadth = 3y. 

New area = x x 3y = 3 xy. 

2 2 

Increase % = 1xy x1x 100 % 

= 50%. 

13. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing 

the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres? 

A.40 B.50 

C.120 D.Data inadequate 

E.None of these 


Answer: Option E 

Explanation: 



Volume 


Let breadth = x metres. 

Then, length = (x + 20) metres. 

Perimeter = 5300 m = 200 m. 

26.50 

2[(x + 20) + x] = 200 

2x + 20 = 100 

2x = 80 

x = 40. 

Hence, length = x + 20 = 60 m. 

14. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If 

the area of the field is 680 sq. feet, how many feet of fencing will be required? 

A.34 B.40 

C.68 D.88 



Explanation: 

We have: l = 20 ft and lb = 680 sq. ft. 

So, b = 34 ft. 

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. 

15. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom 

at 75 paise per sq. m, is: 

A.Rs. 456 B.Rs. 458 

C.Rs. 558 D.Rs. 568 



Explanation: 

Area to be plastered= [2(l + b) x h] + (l x b) 



Volume 


= {[2(25 + 12) x 6] + (25 x 12)} m 2 

= (444 + 300) m 2 

= 744 m 2 . 

Cost of plastering = Rs. 744 x 75 = Rs. 558. 

100 

D. Exercise Problems 

1. A regular hexagon is inscribed in a circle of radius 8 cm. Find the area in circle other than 

hexagon portion 

a)6(2П -√3) 

b)3(2П -√3) 

c)18(2П -√3) 

d)none 

2. Find the area of a rhombus one side of which measures 15cm and one diagonal is 24cm? 

a)512 cm² b)216 cm² 

c)450 cm² d) 309 cm² 

3. Find the area of an isosceles triangle whose equal sides are 8cm each and the third side is 

10cm? 

a)10 cm² b)48 cm² 

c)5√39 cm² 

d)10√10 cm² 

4. A rope 88m long has been bent in the form of a circle. Find the area of the circle? 

a)343 m² b)616 m² 

c)196 m² d)225 m² 

5. The area of a circle is 220sq.cm.What will the area of a square inscribed in this circle will 

be? 

a)110 cm² b)120 cm² 

c)140 cm² d)160 cm² 

6. From a solid right circular cylinder with a height of 10cm and a diameter of the base of 

12cm,a right circular cone of the same height and base is cut off. Find the remaining volume 

of solid? 

a)624.6 cm 3 b)616 cm 3 

c)728.6 cm 3 d)754.28 cm 3 

7. A hollow spherical shell is made of metal of density 4.8g/ cm 3. 

If its internal and external radii are 10cm and 12cm respectively, find the weight of the shell 

a)15.24kg 

b)12.84kg 

c)14.64kg 

d)none 

8. If the average distance of the sun from the earth is 91 x 10 6 miles and the angles subtended 

by the sun at the edge of a person on the earth is 3 minutes, the diameter of the sun in miles is 

approximately 

a)85000 b)632000 

c)73333 d)793722 



Volume 


9. Ramu has bought a field in the shape of a parallelogram with a perimeter of 320m and one 

internal angle=150 0 .If he wants to utilize the maximum area for cultivation ,what should be 

the length of his field? 

a)70,90 

b)80,80 

c)75,85 

d)cannot be computed 

10. The front wheels of a cart cover a distance of 3П m in one revolution and the rear wheels 

cover a distance of 4Пm in one revolution.What will be the distance traveled by the cart 

when the front wheels have made 5 more revolution than the rear ones? 

a)20 b)15 

c)100 d)5 

11. A rectangular carpet has an area of 240 sq.metres.If its diagonal and the longer side 

together are equal to five times the shorter side,what will be the length of the carpet? 

a)5m 

b)10m 

c)12m 

d)24m 

12. If the ratio of the areas of two squares is 16:1, What will be the ratio of their perimeter? 

a)1:16 

b)1:4 

c)4:1 

d)8:1 

13. The length of a rectangle is 1 cm more than its breadth .its perimeter is 14cm.What will 

be the area of the rectangle? 

a)4 cm² b)3 cm² 

c)6 cm² d)12 cm² 

14. If the side of an equilateral triangle is decreased by 20%,its area is decreased by what 

percent? 

a)20% 

b)25% 

c)36% 

d)40% 

15. If the radius of a circle is doubled,by how much percentage does the area increases? 

a)100% 

b)200% 

c)300% 

d)400% 

16. Find the volume of a cube whose surface area is 384sq.cm? 

a)343 cm 3 b)384 cm 3 

c)400 cm 3 d)512 cm 3 

17. The slant height of the frustum of a cone is 20cm and the height of the frustum is 16cm 

.the radius of the smaller circle is 8cm.find the volume of the frustum? 

a)9880 cm 3 b)10459.43 cm 3 

c)11960 cm 3 d)12464 cm 3 

18. What is the total surface area of a cylinder that has been made from a rectangle of length 

12m & breadth 10m? 

a)120 m² b)132 m² 

c)120+25/П m² 

d)none 

19. Triangle ABC is right angled at C.What is the value of 



Volume 


tan A + tan B? 

a)a+b 

c)a²/bc 

b)c²/ab 

d)b²/ac 

20. A rectangle plot has to be fenced on one long side ,one short side and the diagonal.If the 

cost of fencing is Rs.5per metre ,the area of the plot is 1,200 sq.m. and the short side is 30m 

long,how much would be the job cost? 

a)Rs.300 b)400 

c)500 d)600 

21. A man walks at the rate of 6km/hr and crosses a square field diagonally in 9 seconds 

.What is the area of the field? 

a)81m² 

b)112.5m² 

c)121m² 

d)125m² 

22. The ratio of the length and breadth of a rectangular park is 3:2.A man cycles along the 

boundary of the park at a speed of 12km/hr and completes one round in 8min .find the area of 

the park. 

a)143200m² 

b)137900m² 

c)78300m² 

d)153600m² 

23. A room is 13m long ,9 m broad and 10m high .Find the cost of painting the four walls of 

the room at Rs.6 per.sq.m .The doors and windows occupy 32sq.m? 

a)Rs.1331 b)1225 

c)2448 d)3000 

24. A rectangular lawn 45m by 35m has two roads each 5m wide running in the middle of it, 

one parallel to length and the other parallel to the breadth. Find the cost of repairing them at 

rs.1 per sq.m? 

a)Rs.225 b)300 

c)375 d)400 

25. A field is in the form of a trapezium whose parallel sides are 110m and 65m and the 

height between the two parallel side is 56 am.Find the cost of ploughing the field at the rate 

of 70paise per sq.m? 

a)Rs.2250 b)1525 

c)3430 d)5120 

26. ABCD is a quadrilateral where in AC is 15cm . The length of the perpendicular from D 

and B on AC are 5cm and 7cm respectively.What will the area of the quadrilateral be? 

a)90cm² 

b)180cm² 

c)225cm² 

d)45cm² 

27. An equilateral triangle of side 6cm has its corners cut off to form a regular hexagon .What 

will be the area of the hexagon? 

a)9√3cm² 

b)6√3cm² 

c)3√3cm² 

d) √3cm² 



Volume 


28. A circular grassy land has a path 7m wide running round it on the outside. The radius of 

the land is 35m.how many stones of dimensions 20cm x 11cm are required to prove the path? 

a)7000 b)11000 

c)77000 d)10000 

29. The area of the circle circumscribed by a regular hexagon is 2П. What is the area of the 

hexagon? 

a)9√3cm² 

b)6√3cm² 

c)3√3cm² 

d) √3cm² 

30. The minute hand of a clock is 7cm long.What will the area swept by the minute hand in 

15minutes be? 

a)19.25 cm² 

b)38.5 cm² 

c)77 cm² d)none 

31. A powder tin has a square base with sides of 8cm and height 14cm.another powder tin has 

a circular base with a diameter of 8cm and height 14cm.find the difference in their capacities? 

a)9√3cm² 

c)3√3cm² 

b)6√3cm² 

d) None 

32. A large field of 700 hectares is divided in to two parts. The difference of the areas of the 

two parts in one-fifth of the average of the two areas. What is the area of the smaller part in 

hectages? 

a)225 b)280 

c)300 d)315 

33. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for 

each part folded along one set of sides and the same in 38 cm when folded along the other set 

of sides. What is the area of the paper in sq. cm 

a)140 b)240 

c)540 d)None 

34. The cost of carpeting a room 18m long with a carpet 75 cm wide at Rs. 4.50 per metre is 

Rs. 810. The breadth of the room is___mts. 

a)7 b)7.5 

c)8 d)8.5 

35. A courtyard 25 cm long and 16 mts broad is to be paved with bricks of dimensions 20 cm 

by 10 cm. The total number of bricks required is 

a)18000 b)20000 

c)25000 d)None 

36. The length of a rectangle is 20% more than its breadth. What will be the ratio of the area 

of a rectangle to that of a square whose side is equal to the breadth of the rectangle. 



Volume 


a)2:1 

c)6:5 

b)5:6 

d)None 

37. A square and rectangle have equal areas. If their perimeters are p 1 and p 2 respectively, 

then 

a)p 1 p 2 d)None 

38. The diagonal of a square is 4√2 cm. The diagonal of another square whose area is double 

that of the first square is ___ cm. 

a)8 b) 8√2 

c) 4√2 d)16 

39. A rectangular water tank is 80m X 40 m. Water flows into it through a pipe 40 sq.cm at 

the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half 

an hour 

a)3/2 cm 

c)5/8 cm 

b)4/9 cm 

d)None 

40. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is 

equal to the sum of areas of the four walls, the volume of the hall is 

a)720 b)900 

c)1200 d)1800 

41. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. 

Its surface area is___ sq. cm 

a)125 b)236 

c)361 d)486 

42. What is the number of iron rods, each of length 7 mts and diameter 2 cm that can be made 

out of 0.88 cubic metres of iron 

a)100 b)200 

c)300 d)400 

43. A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep 

on the deeper side. Its volume is___ mt. cube 

a)208 b)270 

c)360 d)408 

44. The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm 

and height 60 cm is 



Volume 


a)2:1 

c)4:3 

b)3:2 

d)5:3 

45. A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a 

circular base with diameter 8 cm and height 14 cm. The difference in their capacities is___ 

cu.cms 

a)0 b)132 

c)137.1 d)192 

46. The ratio between the radius of the base and the height of a cylinder is 2:3. If its volume 

is 12936 cu. Cm, the total surface area of the cylinder is____sq.cm 

a)2587.2 b)3080 

c)25872 d)38808 

47. The radius of the cylinder is half its height and area of the inner part is 616 sq.cm. 

Approximately how many litres of milk can it contain 

a)1.4 

c)1.7 

b)1.5 

d)1.9 

48. The sum of the radius of the base and height of a solid cylinder is 37 metres. If the total 

surface area of the cylinder be 1628 sq.metres, it volume is 

a)3180 b)4620 

c)5240 d)None 

49. Two cones have their heights in the ratio 1:3 and radii 3:1. The ratio of their volumes is 

a)1:1 

c)3:1 

b)1:3 

d)2:3 

50. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their 

heights 

a)1:8 

c)2:1 

b)1:4 

d)4:1 



Volume 


SOLUTION TO EXERCISE PROBLEMS: 



Volume 




Volume 




Volume 




Volume 




Volume 




Volume 




Volume 




Volume 




Volume 




Volume 


E. Previous Exam Questions: 

1.If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the 

sphere is___cm. [C.D.S. 2005] 

a)9 cm b)36 cm 

c)54 cm d)81 cm 

2. Spheres A and B have their radii 40 cm and 10 cm respectively. The ratio of the surface 

area of A to the surface area of B is: [Bank P.O. 2000] 

a)1:4 

c)4:1 

b)1:16 

d)16:1 

3. Surface area of a sphere is 2464 sq. cm. If its radius be doubled, then the surface are of the 

new sphere will be [Bank P.O. 2001] 

a)20 b)15 

c)100 d)5 

4.If the radius of a sphere is doubled, how many times does its volume become 

[S.S.C. 2000] 

a)2 times b)4 times 

c)6 times d)8 times 

5.If the radius of a sphere is increased by 2 cm, then it surface area increases by 352 sq. cm. 

The radius of the sphere before the increase was___ cm. 

[C.D.S. 

2006] 

a)3 b)4 

c)5 d)6 

6.If the measured value of the radius is 1.5% larger, the percentage error (correct to one 

decimer place) made in calculating the volume of a sphere is 

[Bank P.O. 2003] 

a)2.1 

c)4.6 

b)3.2 

d)5.4 

7.A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered 

in to the water until it is completely immersed. The water level in the vessel will rise 

by___cm. 

[Infosys 2009] 

a)2/9 

b)4/9 

c)9/4 

d)9/2 



Volume 


8.12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 

2 cm height. The diameter of each sphere is___cm. [C.D.S. 2009] 

a)√3 b)2 

c)3 d)4 

9.A cylinder tub of radius 12 cm contains water upto a depth of 20cm. A spherical iron ball is 

dropped into the tub and thus the level of water is raised by 6.75 cm. The radius of the ball 

is__cm. [C.D.S. 2010] 

a)4.5 b)6 

c)7.25 d)9 

10.The length of a rectangle is halved, while its breadth is tripled. What is the percentange 

change in area [Bank P.O. 2005] 

a)25% increase 

c)50% decrease 

b)50% increase 

d)75% decrease 

11.The length of rectangle is decreased by r% and breadth is increased by (r+5)%. Find r, if 

area of triangle is unaltered. [Bank P.O. 2000] 

a)5 b)8 

c)10 d)15 

12.The length of a rectangle is increased by 60%. By what percent would the width have to 

be decreased so as to maintain the same area [C.D.S. 2011] 

a)75/2 % 

c)75% 

b)60% 

d)120% 

13. The perimeters of five squares are 24 cm, 32 cm 40 cm, 76 cm and 80 cm respectively. 

The perimeter of another square equal in area to the sum of the areas of these squares 

is___cm. 

[S.S.C. 2003] 

a)31 b)62 

c)124 d)961 

14.The number of marble slabe of size 20cm X 30cm required to pave the floor of a square 

room of side 3 mt is 

[Bank P.O. 

2010] 

a)100 b)150 

c)225 d)250 

15. 50 square stone slabs of equal size were needed to cover a floor area of 72 sq.cm. The 

length of each stone slabe is___cm. 

[C.D.S. 

2008] 

a)102 b)120 

c)201 d)210 



Volume 


16.A rectangular room can be partitioned in to two equal square rooms by a partition 7 metres 

long. What is the area of the rectangular room in square metres [Bank P.O. 2005] 

a)49 b)147 

c)196 d)None 

17.The three sides of a triangle are 5cm, 12cm and 13 cm respectively. Then, its area 

is___sq.cm 

[S.S.C. 2000] 

a)10√3 

b)10√6 

c)20 d)30 

18.The sides of a triangle are in the ratio of ½, 1/3, 1/4 . If the perimeter is 52 cm. Then the 

length of the smallest side is____cm. [Bank P.O. 2004] 

a)9 b)10 

c)11 d)12 

19.The area of a triangle is 216 sq.cm and its sides are in the ratio 3:4:5. The perimeter of the 

triangle is___cm. [C.D.S. 2007] 

a)49 b)12 

c)35 d)72 

20.The sides of a triangle are 3cm, 4 cm, and 5 cm. The area of the triangle formed by joining 

the mid-points of the sides of this triangle is [C.D.S. 2006] 

a)3/4 

b)3/2 

c)3 d)6 

21. The slant height of a right circular cone is 10 mts and its height is 8 mts . Find the area of 

its curved surface____sq.mts. [Bank P.O. 2005] 

a)30π 

c)60π 

b)40π 

d)80π 

22. If a right circular cone of height 24 cm has a volume of 1232 cu.cm, then the area of its 

curved surface is___sq.cm [S.S.C. 2008] 

a)154 b)550 

c)704 d)1254 

23.The curved surface of a right circular cone of height 15 cm and base diameter 16 cm 

is___sq.cm [S.S.C. 2002] 

a)60π 

c)120π 

b)68π 

d)136π 



Volume 


24. If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of 

the sphere is____cm. [C.D.S. 2005] 

a)9 b)36 

c)54 d)81 

25. If the radius of a sphere is doubled, how many times does its volume become___times. 

[S.S.C. 2005] 

a)2 b)4 

c)6 d)8 

26. If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 

sq.cm. The radius of the sphere before the increase was___cm. 

[R.R.B. 

2003] 

a)3 b)4 

c)5 d)6 

27. There is a square of side 6 cm . A circle is inscribed inside the square. Find the ratio of 

the area of circle to square. [Honey Well 

2009] 

a) π/5 b) π/4 

c) π/6 d) π/2 

28. One rectangular plate with length 8inches,breadth 11 inches and 2 inches thickness is 

there. What is the length of the circular rod with diameter 8 inches and equal to 

volume of rectangular plate? 

[HCL 

2010] 

a)3.5 

b)4.5 

c)5.5 

d)6.5 

29. If the length of the rectangle is reduced by 20% and breath is increased by 20 % what is 

the net change in % [TCS 2010] 

a)3 b)4 

c)5 d)6 

30. How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 feet 

long & 6feet wide 

[Infosys 

2010] 

a) 24 b)96 

c)3456 d)13824 

31. A warehouse had a square floor with area 10,000 sq.meters. A rectangular addition was 

built along one entire side of the warehouse that increased the floor by one-half as much as 

the original floor. How many meters did the addition extend beyond the original buildings? 



Volume 

A)10 B)20 

C)50 D)200 


[TCS 2011] 

32. A rectangular tank 10" by 8" by 4" is filled with water. If all of the water is to be 

transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller 

tanks are needed? 

A. 9 B. 12 [Infosys 2011] 

C. 16 D. 21 

Key to Exercise Problems:- 

1.d 2.b 3.c 4.b 5.c 6.d 7.c 8.d 9.b 10.a 

11.d 12.c 13.d 14.c 15.c 16.d 17.b 18.d 19.b 20.d 

21.b 22.d 23.c 24.c 25.c 26.a 27.b 28.c 29.c 30.b 

31.a 32.d 33.a 34.a 35.b 36.c 37.a 38.a 39.c 40.c 

41.b 42.d 43.b 44.c 45.d 46.b 47.b 48.b 49.c 50.b 

Key to Previous Exam Questions:- 

1.d 2.d 3.b 4.d 5.d 6.c 7.c 8.d 9.d 10.b 

11.e 12.a 13.c 14.c 15.b 16.d 17.d 18.d 19.d 20.b 

21.c 22.b 23.d 24.c 25.d 26.d 27.b 28.a 29.b 30.a 

31.c 32.b

CALCULATION OF AREA, SURFACE AREA AND VOLUME

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