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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?

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**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 = 2πr πrh Surface area of a cylinder. = 2π(60) π(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

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**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 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.

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**Find the height of a cylinder**

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

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**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 = 2πr πrh Surface area of a cylinder. = 2π(60) π(10)18 Substitute known values. = cm2 Use a calculator.

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**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.

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**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

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EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.

EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.

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