Presentation on theme: "EXAMPLE 3 Find the height of a cylinder COMPACT DISCS"— Presentation transcript:
1EXAMPLE 3Find the height of a cylinderCOMPACT DISCSYou 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?
2Find the height of a cylinder EXAMPLE 3Find the height of a cylinderSOLUTIONThe 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 πrhSurface area of a cylinder.= 2π(60) π(60)(24)Substitute known values.≈ 31,667Use a calculator.You will need at least 31,667 square millimeters, or about 317 square centimeters of shrink wrap.ANSWER
3Find the height of a cylinder EXAMPLE 4Find the height of a cylinderFind the height of the right cylinder shown, which has a surface area of square meters.SOLUTIONSubstitute known values in the formula for the surface area of a right cylinder and solve for the height h.S = 2πr2 + 2πrhSurface area of acylinder.
4Find the height of a cylinder EXAMPLE 4Find the height of a cylinder= 2π(2.5)2 + 2π(2.5)hSubstitute knownvalues.= 12.5π + 5πhSimplify.– 12.5π = 5πhSubtract 12.5π fromeach side.≈ 5πhSimplify. Use acalculator.7.5 ≈ hDivide each side by5π.The height of the cylinder is about 7.5 meters.ANSWER
5GUIDED 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.SOLUTIONS = 2πr πrhSurface area of a cylinder.= 2π(60) π(10)18Substitute known values.= cm2Use a calculator.
6GUIDED PRACTICE for Examples 3 and 4 4. Find the radius of a right cylinder with height 5 feet and surface area 208π square feet.SOLUTIONS = 2πr2 + 2πrhSurface area of a cylinder.208π =2π(r)2 + 2πr(5)Substitute known value.208π = 2πr2 + 10πrSimplify.104 = r2 +5rDivide 2π from each side.
7The radius of cylinder is 8 feet. ANSWER GUIDED PRACTICEfor Examples 3 and 4r = 8Simplify. Use a calculator.The radius of cylinder is 8 feet.ANSWER