Surface Area

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$Math and Chemistry - McGraw-Hill Ryerson$

4. a) The cylinder has two identical circles, one at each end.What is the area of each circle?b) What is the area of the rectangle?c) The total surface area is the sum of the areas of all the shapes.What is the surface area of the glow stick? Include the units inyour final answer.Pop cans arecylinders. The world’slargest Coke can islocated in Portage laPrairie, Manitoba.Reflect on Your Findings5. a) How would you find the surface area of any right cylinder?b) What type of units do you use to measure surface area?Example 1: Determine the Surface Area of a Right Cylindera) Estimate the surface area of the can.b) What is the surface area of the can? Expressyour answer to the nearest hundredth of asquare centimetre?11 cmSolution7.5 cmThe surface area of the can is found by adding the areas of the twocircular bases and the rectangular side that surrounds them.The width, w, of the rectangle is the height of the can.The length, l, of the rectangle is equal to the circumference of the circle.a) To estimate, use approximate values: d ≈ 8 cm, w ≈ 10 cm, π ≈ 3.Area of circle = π × r 2≈ 3 × 4 × 4≈ 48There are two circles: 2 × 48 = 96The area of the two circles is approximately 96 cm 2 .Area of rectangle = l × w= (π × d) × w Replace l with the formula for the≈ 3 × 8 × 10 circumference of a circle.≈ 240The area of the rectangle is approximately 240 cm 2 .Estimated surface area = area of two circles + area of rectangle≈ 96 + 240≈ 340The estimated surface area is 340 cm 2 .r 2 meansr × rThe radius of a circleis half the diameter.LiteracyLinkcircleradiuscentrediameterThe formula for thecircumference of a circle isC = π × d or C = 2 × π × r.5.4 Surface Area of a Cylinder • MHR 25
StrategiesDraw a DiagramRefer to page xxx.b) Method 1: Use a NetDraw the net and label the measurements.top side bottom7.5 cm11 cmThe diameter of the circle is 7.5 cm.Determine the radius.7.5 ÷ 2 = 3.75The radius of the circle is 3.75 cm.Round youranswer at the end ofthe calculation.Find the area of one circle.A = π × r 2Use 3.14 as anapproximate valueA ≈ 3.14 × 3.75 2for π.A ≈ 44.15625The area of one circle is approximately 44.15625 cm 2 .Find the area of two circles.2 ×44.15625 = 88.3125The area of both circles is approximately 88.3125 cm 2 .Find the area of the rectangle using the circumference of the circle.A = l × wA = (π × d) × w Replace l with the formula for the circumference of a circle.A ≈ 3.14 × 7.5 × 11A ≈ 259.05The area of the rectangle is approximately 259.05 cm 2 .Calculate the total surface area.Total surface area = 88.3125 + 259.05= 347.3625The total surface area is approximately 347.36 cm 2 .26 MHR • Chapter 5
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Page 27 and 28: • The surface area of a cylinder
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