Presentation on theme: "EXAMPLE 3 Find the height of a cylinder COMPACT DISCS"— Presentation transcript:
1 EXAMPLE 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?
2 Find 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
3 Find 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.
4 Find 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
5 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.SOLUTIONS = 2πr πrhSurface area of a cylinder.= 2π(60) π(10)18Substitute known values.= cm2Use a calculator.
6 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.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.
7 The 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