 # Do Now 1.) 2). 5/15/2014 10-3 C Surface Area of Cylinders.

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Do Now 1.) 2)

5/15/2014 10-3 C Surface Area of Cylinders

Parts of a cylinder A cylinder has 2 main parts. A rectangle and A circle – well, 2 circles really. Put together they make a cylinder.

The Soup Can Think of the Cylinder as a soup can. You have the top and bottom lid (circles) and you have the label (a rectangle – wrapped around the can). The lids and the label are related. The circumference of the lid is the same as the length of the label.

Area of the Circles Formula for Area of Circle A=  r 2 = 3.14 x 3 2 = 3.14 x 9 = 28.26 But there are 2 of them so 28.26 x 2 = 56.52 units squared

The Rectangle This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy. Notice that the base is the same as the distance around the circle (or the Circumference).

Key Concept

Example 2 Find the surface area of the cylinder. Use 3.14 for . Round to the nearest tenth. Since the diameter of the cylinder is 12 meters, use 6 meters for the radius. S.A. = 2πrh + 2πr 2 S.A. ≈ 2(3.14)(6)(8) + 2(3.14)(6) 2 S.A. ≈ 301.44 + 226.08 S.A. ≈ 527.52 The surface area is about 527.5 square meters.

Example 3 A candle is 8 centimeters tall and has a diameter of 4 centimeters. It has a paper label around its side only. Find the area of the candle that is covered by the label. Round to the nearest tenth. Since only the side of the cylinder is covered by the label, the formula is adjusted so that only the curved surface is found. S.A. = 2πrhArea of the curved surface of a cylinder

Answer: The area covered by the label is about 100.5 square centimeters. S.A. ≈ 2(3.14)(2)(8) Replace r with 2 and h with 8. S.A. ≈ 100.48 Simplify.

Example 4 SA = (  d x h) + 2 (  r 2 ) = (3.14 x 22 x 14) + 2 (3.14 x 11 2 ) = (367.12) + 2 (3.14 x 121) = (967.12) + 2 (379.94) = (967.12) + (759.88) = 1727 cm 2