Calculating Shrink Wrap Needed for a Stack of 20 Compact Discs
To cover a stack of 20 cylindrical compact discs with a height of 1.2 mm and a radius of 60 mm using shrink wrap, we must calculate the minimum surface area required. The total height of the stack is 24 mm. Using the formula for the surface area of a cylinder (S = 2πr² + 2πrh), we substitute the values to find that approximately 31,667 square millimeters, or about 317 square centimeters, of shrink wrap is needed. This calculation ensures complete coverage for the discs.
Calculating Shrink Wrap Needed for a Stack of 20 Compact Discs
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You are wrapping a stack of 20 compact discs using a shrink wrap. Each disc is cylindrical with height 1.2millimeters and radius 60millimeters. What is the minimum amount of shrink wrap needed to cover the stack of 20 discs? EXAMPLE 3 Find the height of a cylinder COMPACT DISCS
ANSWER You will need at least 31,667square millimeters, or about 317square centimeters of shrink wrap. 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 60millimeters. 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.
Find the height of the right cylinder shown, which has a surface area of 157.08square meters. EXAMPLE 4 Find the height of a cylinder 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.
ANSWER The height of the cylinder is about 7.5meters. EXAMPLE 4 Find the height of a cylinder Substitute known values. 157.08 = 2π(2.5)2 + 2π(2.5)h 157.08 = 12.5π + 5πh Simplify. Subtract 12.5π from each side. 157.08 – 12.5π = 5πh 117.81 ≈ 5πh Simplify. Use a calculator. 7.5 ≈ h Divide each side by 5π.
GUIDED PRACTICE for Examples 3 and 4 3. Find the surface area of a right cylinder with height 18centimeters and radius 10centimeters. 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 height5 feet and surface area 208πsquare feet. SOLUTION Surface area of a cylinder. S = 2πr2 + 2πrh 208π =2π(r)2+ 2πr(5) Substitute known value. 208π = 2πr2 + 10πr Simplify. Divide 2π from each side. 104 = r2 +5r
ANSWER The radius of cylinder is 8feet. GUIDED PRACTICE for Examples 3 and 4 r = 8 Simplify. Use a calculator.
