EXAMPLE 3 Find the height of a cylinder COMPACT DISCS

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Presentation transcript:

EXAMPLE 3 Find the height of a cylinder COMPACT DISCS You are wrapping a stack of 20 compact discs using a shrink wrap. Each disc is cylindrical with height 1.2 millimeters and radius 60 millimeters. What is the minimum amount of shrink wrap needed to cover the stack of 20 discs?

Find the height of a cylinder EXAMPLE 3 Find the height of a cylinder SOLUTION The 20 discs are stacked, so the height of the stack will be 20(1.2) = 24 mm. The radius is 60 millimeters. The minimum amount of shrink wrap needed will be equal to the surface area of the stack of discs. S = 2πr2 + 2πrh Surface area of a cylinder. = 2π(60)2 + 2π(60)(24) Substitute known values. ≈ 31,667 Use a calculator. You will need at least 31,667 square millimeters, or about 317 square centimeters of shrink wrap. ANSWER

Find the height of a cylinder EXAMPLE 4 Find the height of a cylinder Find the height of the right cylinder shown, which has a surface area of 157.08 square meters. SOLUTION Substitute known values in the formula for the surface area of a right cylinder and solve for the height h. S = 2πr2 + 2πrh Surface area of a cylinder.

Find the height of a cylinder EXAMPLE 4 Find the height of a cylinder 157.08 = 2π(2.5)2 + 2π(2.5)h Substitute known values. 157.08 = 12.5π + 5πh Simplify. 157.08 – 12.5π = 5πh Subtract 12.5π from each side. 117.81 ≈ 5πh Simplify. Use a calculator. 7.5 ≈ h Divide each side by 5π. The height of the cylinder is about 7.5 meters. ANSWER

GUIDED PRACTICE for Examples 3 and 4 3. Find the surface area of a right cylinder with height 18 centimeters and radius 10 centimeters. Round your answer to two decimal places. SOLUTION S = 2πr2 + 2πrh Surface area of a cylinder. = 2π(60)2 + 2π(10)18 Substitute known values. = 1759.29 cm2 Use a calculator.

GUIDED PRACTICE for Examples 3 and 4 4. Find the radius of a right cylinder with height 5 feet and surface area 208π square feet. SOLUTION S = 2πr2 + 2πrh Surface area of a cylinder. 208π =2π(r)2 + 2πr(5) Substitute known value. 208π = 2πr2 + 10πr Simplify. 104 = r2 +5r Divide 2π from each side.

The radius of cylinder is 8 feet. ANSWER GUIDED PRACTICE for Examples 3 and 4 r = 8 Simplify. Use a calculator. The radius of cylinder is 8 feet. ANSWER