Geometry & Spatial Sense – Practice Problems

Geometry & Spatial Sense – Practice Problems
Surface Area & Volume
1.
If the sphere shown above has a radius of 18 units, then what is the volume of the sphere?
A. 7,776 cubic units
B. 9,720 cubic units
C. 1,296 cubic units
D. 3,888 cubic units
Measurement Problems
2. Compute the following.
11 lb 6 oz - 8 lb 11 oz
A. 2 lb 5 oz
B. 3 lb 11 oz
C. 2 lb 11 oz
D. 3 lb 12 oz
Measurement Problems
3. Susie is pouring water into a tub. She pours 5 gallons, 5 cups, 8 pints, and 5 quarts of water
into the tub. How much water has Susie poured into the tub?
A. 126 cups
B. 62 cups

C. 81 cups
D. 121 cups
Similar Figures
4. Amanda is resizing a rectangular picture on her computer. The original picture has a width of
8 in and a length of 5 in. If she wants to keep it proportional, but have the new width be 4 in,
what should be the new length?
A. 10.0 in
B. 2.0 in
C. 7.5 in
D. 2.5 in
Properties of Polygons
5. Find the measure of one interior angle of a regular polygon with nine sides.
A. 280°
B. 70°
C. 1,260°
D. 140°
Geometric Patterns
6.
Look at Koch's Snowflake above. What would it look like after one more iteration?
W. X.

Y. Z.
A. Y
B. W
C. Z
D. X
Surface Area & Volume
7.
If X = 4 units, then what is the volume of the cube shown above?
A. 128 cubic units
B. 36 cubic units
C. 64 cubic units
D. 39 cubic units
Pythagorean Theorem
8.
*Note: Figure not drawn to scale.
If Y = 5 cm and Z = 13 cm, what is the length of X?
A. 12 cm

B. 9 cm
C. 13 cm
D. 11 cm
Object Transformations
9. Which of the following transformations will produce a figure that is similar, but not congruent,
to the original figure?
A. dilation
B. reflection
C. translation
D. rotation
Nets & Projective Views
10. Which of the four nets shown below can be folded into a triangular prism?
W. X.
Y. Z.
A. Z
B. Y
C. X
D. W
Geometric Patterns

11. Which of the following shapes show self-similarity?
W. X.
Y. Z.
A. X and Y
B. X and Z
C. X, Y, and Z
D. W and X
Geometric Patterns
12.
An oval-shaped pink bead is inserted next to each circle-shaped aqua bead in the necklace. Using
this new pattern, if a necklace is made with 120 beads, how many pattern segments will the
necklace have?
A. 21 with 4 left over
B. 20 with 2 left over
C. 20
D. 17

Object Transformations
13.
The translation above shows an object moving ______________.
A. 8 units to the right and 3 units down
B. 8 units to the right and 2 units down
C. 9 units to the right and 3 units down
D. 9 units to the right and 2 units down
Properties of Polygons
14. What is the main difference between a square and a rhombus?
A. A square has sides that are parallel, but a rhombus does not.
B. A rhombus is always bigger than a square.
C. A rhombus has 4 right angles, but a square does not.
D. A square must have 4 right angles, but a rhombus may or may not.
Pythagorean Theorem
15.
Is S = 7 cm and T = 24, what is the length of R?

31 cm
A.
28 cm
B.
23 cm
C.
25 cm
D.
Geometric Patterns
16. Determine the number of iterations that created the Koch's Snowflake below.
A. 2
B. 3
C. 1
D. 4
Geometric Patterns
17.
In the pattern sequence above there are five shapes. If this pattern is repeated for a total of 64
shapes, what would be the final shape?
A. hexagon
B. square
C. diamond
D. octagon

Properties of Polygons
18. Find the measure of one interior angle of a regular octagon.
A. 270°
B. 1,080°
C. 135°
D. 180°
Perimeter & Area
19.
Note: Figure not drawn to scale.
If X = 7 units, Y = 13 units, and Z = 14 units, then what is the perimeter of the triangle shown
above?
A. 28 units
B. 33 units
C. 30 units
D. 34 units
Similar Figures
20.

Note: Figures are not drawn to scale.
Right triangle ABC is similar to right triangle DEF. If the measure of angle A is 33°, what is the
measure of angle F?
A. 147°
B. 57°
C. 33°
D. 89°
Similar Figures
21.
Note: Figures not drawn to scale.
In the picture above, KLMN ~ XYZW. If K = 8 m, L = 5 m, M = 7 m,
N = 13 m, and Z = 10.5 m, then what is the length of Y?
A. 19.5 m
B. 7.5 m
C. 12 m
D. 13.5 m
Geometric Patterns
22. At each iteration in the Sierpinski Triangle, the area of the original is changed by how much?
The first 3 iterations of Sierpinski's Triangle look like this:

A. increased by 75%
B. reduced by 50%
C. reduced by 25%
D. increased by 25%
Similar Figures
23.
Note: Figure is not drawn to scale.
The rectangle above has the dimensions 31 cm by 19 cm.
Which set of dimensions would produce a similar figure?
A. 31 cm by 95 cm
B. 165 cm by 95 cm
C. 155 cm by 19 cm
D. 155 cm by 95 cm
Pythagorean Theorem
24. The city of Nairobi, Kenya, is 470 km east and 185 km south of the city of Kampala,
Uganda. If Matunde is flying from Nairobi to Kampala, what is the shortest possible distance of
his flight? (Round to the nearest km.)
A. 505 km
B. 432 km
C. 655 km
D. 563 km

Perimeter & Area
25. A cylinder with a radius of 6 in, a height of 15 in, and its cross section are shown below.
Note: Figure not drawn to scale.
What is the area of the cross section shown?
A.
B.
C.
D.
Geometric Patterns
26. The Iterated Function System (IFS)
A. is the result of geometric calculations.
B. includes a system to determine the area of a geometric figure.
C. is the means to stop geometric patterns from growing.
D.
involves a simple transformation done to an object or shape that is repeatedly done on
resulting object or shape.
Perimeter & Area
27.

What is the approximate area of the figure above?
A. 12
B. 8 1 / 2
C. 15 1 / 2
D. 10
Properties of Polygons
28. The vertices of a quadrilateral are located at (0, -2), (5, -2), (5, 6), and (0, 6).
Which of the following classifies this quadrilateral?
A. The quadrilateral is a square.
B. The quadrilateral is a trapezoid.
C. The quadrilateral is a rhombus.
D. The quadrilateral is a rectangle.
Nets & Projective Views
29. A 2-dimensional net is shown below.
Which of the following 3-dimensional shapes can be formed with this net?
A. rectangle
B. circle
C. cylinder

D. cone
Surface Area & Volume
30.
If the volume of the smaller cylinder is 36 in 3 , what is the volume of the larger cylinder?
(Volume = r 2 h)
A. 108 in 3
B. 72 in 3
C. 144 in 3
D. 180 in 3
Perimeter & Area
31.
16 units
9 units
What is the perimeter of the rectangle above?
A. 59 units
B. 25 units
C. 144 units
D. 50 units

Perimeter & Area
32.
If the area of the smaller rectangle is 30 inches 2 , what is the area of the larger rectangle?
A. 120 inches 2
B. 90 inches 2
C. 60 inches 2
D. 240 inches 2
Measurement Problems
33. Compute the following.
4.997 kL - 5,396 cL
A. 399 cL
B. 5,391.003 cL
C. 494,304 cL
D. 4,896.3 cL
Pythagorean Theorem
34.
*Note: Figure not drawn to scale.

If Y = 8 ft and Z = 100 ft, what is the length of X?
A. 28 ft
B. 5 ft
C. 136 ft
D. 6 ft
Pythagorean Theorem
35.
*Note: Figure not drawn to scale.
If X = 9 cm and Y = 12 cm, what is the length of Z?
A. 15 cm
B. 13 cm
C. 14 cm
D. 18 cm
Surface Area & Volume
36.
Note: Figure not drawn to scale
If h = 15 units and r = 5 units, what is the volume of the cone shown above? Use 3.14 for .

A. 78.5 cubic units
B. 235.5 cubic units
C. 392.5 cubic units
D. 1,177.5 cubic units
Surface Area & Volume
37.
Note: Figure not drawn to scale
If l = 9 units, w = 8 units, and h = 17 units, what is the surface area of the rectangular prism
shown above?
A. 790 square units
B. 1,224 square units
C. 361 square units
D. 722 square units
Similar Figures
38. Rectangle ABDE and rectangle CDEF are similar.
What is the length of AE?
A.

B.
C.
D.
Perimeter & Area
39.
If the area of the smaller circle is 4 inches 2 , what is the area of the larger circle?
A. 8 inches 2
B. 12 inches 2
C. 16 inches 2
D. 24 inches 2
Geometric Patterns
40.
A necklace contains 100 beads. A section of it is shown above. If the pattern shown continues to
repeat itself in the necklace, how many circle-shaped aqua beads are in the necklace?
A. 90
B. 95
C. 19

D. 20
Object Transformations
41.
Which graph shows a reflection across the x-axis?
A. IV
B. III
C. II
D. I
Nets & Projective Views
42.
Which solid is represented by the top, front, and side views above?

A. Z
B. W
C. Y
D. X
Measurement Problems
43. Paul is measuring pieces of wood in order to build a shelf. The first piece of wood measured
4 feet and 7 inches. The second piece of wood measures 2 feet and 5 inches. The third piece of
wood measures 2 feet and 8 inches. How much wood does Paul have altogether?
A. 9 feet 8 inches
B. 28 feet
C. 11 feet 2 inches
D. 7 feet 8 inches
Object Transformations
44.
Lisa is drawing triangle STU that is a dilation from point (6,5) of triangle PQR. She has already
drawn points S and T.

At what coordinates should she plot point U, of triangle STU?
A. (6,-1)
B. (6,1)
C. (-3,-1)
D. (6,-4)
Measurement Problems
45. Jody juggled for 4 days and 6 hours. How many minutes did Jody juggle?
A. 420 minutes
B. 4.6 minutes
C. 6,120 minutes
D. 10 minutes
Pythagorean Theorem
46. Anthony was mapping out a route to ride his bike. The route he picked forms a right triangle,
as shown in the picture below.
If the route takes him 5 miles on Forrest Lane and 13 miles up Cedar Drive, how far will
Anthony ride down Pine Avenue?
A. 18 miles
B. 8 miles
C. 12 miles
D. 15 miles
Nets & Projective Views

47.
Which solid is represented by the front, side, and top views above?
A. Y
B. X
C. W
D. Z
Perimeter & Area
48.
Note: Figure not drawn to scale.
If X = 13 units and h = 7 units, then what is the area of the triangle shown above?
A. 182 square units
B. 24.5 square units

C. 45.5 square units
D. 91 square units
Object Transformations
49.
Which graph below shows a rotation of the object in the graph above about point (-2, 3)?
A. II
B. IV
C. I
D. III
Similar Figures
50.

Note: Figure is not drawn to scale.
The rectangle above has the dimensions 11 yd by 34 yd.
Which set of dimensions would produce a similar figure?
A. 87 yd by 238 yd
B. 11 yd by 238 yd
C. 77 yd by 34 yd
D. 77 yd by 238 yd
Measurement Problems
51. Compute the following.
77.8 mg + 0.781 kg
A. 78.581 g
B. 78,581 g
C. 78.878 g
D. 781.0778 g
Properties of Polygons
52. Which of the following is a quadrilateral that will always have 4 equal sides and 4 right
angles?
A. rectangle
B. trapezoid
C. rhombus
D. square
Pythagorean Theorem

53. Find the area of the right triangle pictured below.
*triangle not drawn to scale
12 in
11 in
A. 5.5 in 2
B. 52.75 in 2
C. 26.38 in 2
D. 89.53 in 2
Surface Area & Volume
54.
Note: Figure not drawn to scale
If l = 13 units, w = 8 units, and h = 4 units, what is the volume of the rectangular prism shown
above?
A. 832 cubic units
B. 416 cubic units
C. 376 cubic units
D. 208 cubic units
Surface Area & Volume
55.

Note: Figure is not drawn to scale
If x = 5 units, y = 6 units, z = 9 units, and h = 4 units, then what is the surface area of the
triangular prism shown above?
A. 168 units 2
B. 192 units 2
C. 96 units 2
D. 105 units 2
Perimeter & Area
56.
4 units
What is the area of the rectangle above?
A. 20 square units
B. 64 square units
C. 40 square units
D. 80 square units
16 units
Geometric Patterns
57. Which of the following shapes show self-similarity?

W. X.
Y. Z.
A. W, X, and Y
B. Y and Z
C. X, Y, and Z
D. X and Z
Similar Figures
58.
Note: Figures are not drawn to scale.
Triangles ABC and DEF are similar figures. If the length of side AC is 14 units, the length of
side BC is 8 units, and the length of side DF is 126 units, what is the length of side EF?
A. 63 units
B. 80 units
C. need more information
D. 72 units
Similar Figures

59.
Note: Figures not drawn to scale.
In the picture above, KLMN ~ XYZW. If m K = 140°, m L = 109°, m M = 56°,
and m N = 55°, then what is the measure of W?
A. 109°
B. 56°
C. 132°
D. 55°
Perimeter & Area
60. The diagram shows isosceles triangle STU. Each vertex of triangle STU is a point on circle V.
If the area of circle V is
sq units, what is the area of triangle STU?
A.
B.
C.
D.

Pythagorean Theorem
61.
*Note: Figure not drawn to scale.
If X = 5 cm and Y = 12 cm, what is the length of Z?
A. 13 cm
B. 12 cm
C. 10 cm
D. 11 cm
Nets & Projective Views
62.
The pictures above represent the front and side views of which of the objects below?
W. X. Y. Z.
A. X

B. Y
C. W
D. Z
Similar Figures
63.
Note: Figures not drawn to scale.
In the picture above, PQRST ~ VZYXW. If m P = 95°, m Q = 78°, m R = 224°, m S
= 36°, and m T = 107°, then what is the measure of W?
A. 224°
B. 107°
C. 78°
D. 36°
Pythagorean Theorem
64. Find the perimeter of the right triangle pictured below.
*triangle not drawn to scale
7 cm
25 cm
A. 56 cm
B. 26 cm
C. 58 cm
D. 84 cm
Surface Area & Volume

65.
Note: Figures are not drawn to scale
The pyramid and prism above have the same L, W, and H. The volume of the pyramid is 18 cm 3 .
What is the volume of the prism?
A. 36 cm 3
B. 6 cm 3
C. 12 cm 3
D. 54 cm 3
Properties of Polygons
66. Alan is building a sign to put in front of his office building.
The sign has 6 sides.
The sign has 3 diagonals coming from each vertex.
The sum of the sign's interior angles equals 720°.
What shape is Alan's sign?
A. octagon
B. hexagon
C. pentagon
D. rectangle
Object Transformations
67.

Which of the following describes the transformations performed on the object shown above?
The object was reflected across the x-axis and shifted 7 units in the x direction and -5 units
A. in the y direction.
B.
C.
D.
The object was reflected across the y-axis and shifted 1 unit in the x direction and -7 units
in the y direction.
The object was reflected across the y-axis and shifted -1 unit in the x direction and -7 units
in the y direction.
The object was reflected across the x-axis and shifted 9 units in the x direction and -3 units
in the y direction.
Measurement Problems
68. Compute the following.
5 ft 3 in + 7 ft 11 in
A. 11 ft 8 in
B. 12 ft 2 in
C. 13 ft 8 in
D. 13 ft 2 in
Nets & Projective Views
69.

W. X. Y. Z.
Which of the objects above have the following front view?
A. X, Y, and Z
B. W and X
C. X and Y
D. W, X, and Y
Properties of Polygons
70. The vertices of a quadrilateral are located at (-3, 2), (1, 5), (5, 2), and (1, -1).
Which of the following classifies this quadrilateral?
A. The quadrilateral is a rectangle.
B. The quadrilateral is a trapezoid.
C. The quadrilateral is a rhombus.
D. The quadrilateral is a square.
Nets & Projective Views
71. The drawing represents a 3-dimensional figure.
Which of the following represent the left and front views of the figure?

W. X.
Y. Z.
A. Z
B. X
C. W
D. Y
Nets & Projective Views
72.
The pictures above represent the front, side, and top views of which of the objects below?
A. Y
W. X. Y. Z.

B. Z
C. W
D. X
Nets & Projective Views
73. Which of the four nets shown below can be formed into a cone?
W. X. Y. Z.
A. X
B. Y
C. Z
D. W
Surface Area & Volume
74.
Note: Figure is not drawn to scale.
If x = 5 units and y = 9 units, then what is the volume of the square pyramid shown above?
A. 150 cubic units
B. 225 cubic units
C. 75 cubic units
D. 125 cubic units
Similar Figures
75.

Note: Figure is not drawn to scale.
The triangle above has side lengths of 30 mm and 38 mm.
Which set of dimensions would produce a similar figure?
A. 150 mm, 195 mm
B. 150 mm, 5 mm
C. 150 mm, 190 mm
D. 150 mm, 38 mm
Properties of Polygons
76.
Which of the following shapes is shown above?
A. square
B. rectangle
C. trapezoid
D. parallelogram
Nets & Projective Views
77.

Which of the following set of pictures represents a side and the bottom view of this solid?
A.
B.
C.
D.
Similar Figures
78.
Note: Figures are not drawn to scale.
Rectangles ABCD and EFGH are similar figures because angles A, B, C, and D are congruent to
angles E, F, G, and H, respectively.
If DA equals 16 units, AB equals 7 units, and HE equals 112 units, what does EF equal?
A. 7 units
B. 256 units
C. 103 units
D. 49 units
Nets & Projective Views
79. Which of the four nets shown below can be folded into a triangular prism?

W. X.
Y. Z.
A. Z
B. Y
C. W
D. X
Properties of Polygons
80. Find the measure of one interior angle of a regular pentagon.
A. 540°
B. 108°
C. 90°
D. 27°
Measurement Problems
81. Billy and his sister, Sarah, are competing to see who can throw their football the farthest.
Billy threw the football 32 yards. Sarah threw the football 1,136 inches. How much farther than
Sarah did Billy throw the football?
A. 97.6 inches
B. 23 inches
C. 16 inches

D. 20 inches
Surface Area & Volume
82.
Note: Figure not drawn to scale.
Heights (Y and Z) have been rounded for computational ease.
If X = 4 units, Y = 3.5 units, and Z = 3.5 units, then what is the surface area of the right
triangular pyramid shown above?
A. 28 square units
B. 49 square units
C. 36 square units
D. 64 square units
Properties of Polygons
83.
Find the sum of the interior angles of the polygon shown above.
A. 540°
B. 720°
C. 900°
D. 360°
Properties of Polygons

84. The interior angles of a polygon equal 180°. How many sides does this polygon have?
A. 2
B. 4
C. 3
D. 5
Geometric Patterns
85.
If the 7-bead segment above is repeated several times to create a necklace with 70 beads, how
many oval-shaped beads will the necklace have?
A. 10
B. 30
C. 18
D. 20
Object Transformations
86.
The translation above shows the object moving ______________.
A. 6 units to the left and 5 units up

B. 3 units to the left and 8 units up
C. 3 units to the right and 8 units down
D. 8 units to the right and 3 units down
Perimeter & Area
87.
7 in.
What is the circumference of the circle?
A. 21.98 in
B. 153.86 in
C. 43.96 in
D. 87.92 in
Measurement Problems
88. Compute the following.
67.6 cm + 81 mm
A. 75.16 cm
B. 87.76 cm
C. 148.6 cm
D. 75.7 cm
Surface Area & Volume
89.

Note: Figure not drawn to scale.
If W = 40 units, X = 28 units, Y = 50 units, and Z = 52 units, then what is the surface area of the
right rectangular pyramid shown above?
A. 4,576 units 2
B. 8,032 units 2
C. 2,848 units 2
D. 3,456 units 2
Geometric Patterns
90.
In the pattern above, how many blue dots will the diagram have in position 2?
A. 2
B. 3
C. 5
D. 4
Object Transformations
91.

If the figure above was rotated 180° counter-clockwise about point A, where would point B on
the figure be plotted?
A. (0,-3)
B. (1,6)
C. (2,-3)
D. (6,2)
E. (6,1)
Object Transformations
92. Which of the following transformations will always produce a congruent figure?
A. translation
B. enlargement
C. dilation
D. reduction
Object Transformations
93.
The translation above shows an object moving ______________.

A. 5 units to the left and 7 units up
B. 7 units to the right and 5 units down
C. 5 units to the left and 7 units down
D. 5 units to the right and 7 units up
Pythagorean Theorem
94. The figure shows some of the dimensions of a parallelogram.
Note: Figure not drawn to scale
What is h, the height of the parallelogram?
A. 17 cm
B. 24 cm
C. 12 cm
D. 6 cm
Perimeter & Area
95.
What is the approximate area of the figure above?
A. 11
B. 12 1 / 2

C. 8
D. 9
Measurement Problems
96. Compute the following.
2 c 5 fl oz + 5 c 6 fl oz
A. 8 c 7 fl oz
B. 7 c 3 fl oz
C. 8 c 3 fl oz
D. 8 c 9 fl oz
Object Transformations
97. Parallelogram JKLM has the coordinates J (1, 8), K (11, 8), L (10, 2), and M (0, 2). Which of
the following sets of points represents a dilation from the origin of parallelogram JKLM?
A. J' (4, 8), K' (44, 8), L' (40, 2), M' (0, 2)
B. J' (5, 12), K' (15, 12), L' (14, 6), M' (4, 6)
C. J' (4, 32), K' (44, 32), L' (40, 8), M' (0, 8)
D. J' (1, 32), K' (44, 8), L' (40, 2), M' (0, 8)
Pythagorean Theorem
98. Benton has an extension ladder than can only be used at a length of 10 feet, 15 feet, or 20
feet. He places the base of the ladder 9 feet from the wall and needs the top of the ladder to reach
12 feet. Which ladder length would Benton need to use to reach this height on the wall?
A. 10 feet
B. 15 feet
C. 20 feet
D. None of these ladder lengths would reach this height.
Measurement Problems

99. A diver has 2,000 psi (pounds per square inch) in his dive tank at the beginning of a dive.
The end reading was 1,000 psi after a dive time of 15 minutes. At what rate was the pressure in
the dive tank decreasing?
A. 66.67 psi/min
B. 133.33 psi/min
C. 200 psi/min
D. |Round(10000*(a+c+e)/(b+d+d+1))/100| miles per hour
Pythagorean Theorem
100.
If L = 65 cm and J = 33 cm, what is the length of K?
56 cm
A.
55 cm
B.
65 cm
C.
73 cm
D.
Answers
1. A
2. C
3. D
4. D
5. D
6. C
7. C

8. A
9. A
10. B
11. A
12. C
13. D
14. D
15. D
16. C
17. D
18. C
19. D
20. B
21. B
22. C
23. D
24. A
25. A
26. D
27. A
28. D
29. C
30. C
31. D
32. A
33. C
34. D
35. A
36. C
37. D
38. C
39. C
40. D
41. D
42. D
43. A
44. A
45. C
46. C
47. D
48. C
49. B
50. D
51. D
52. D
53. C

54. B
55. A
56. B
57. B
58. D
59. D
60. A
61. A
62. A
63. B
64. A
65. D
66. B
67. C
68. D
69. D
70. C
71. A
72. C
73. C
74. C
75. C
76. D
77. D
78. D
79. D
80. B
81. C
82. A
83. A
84. C
85. D
86. B
87. C
88. D
89. A
90. B
91. E
92. A
93. A
94. C
95. A
96. C
97. C
98. B

99. A
100. A