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If the radius and height of a cone are increased by 200% and 100% respectively by what percentage does the volume of the cone increase?
If the radius and height of a cone are increased by 200% and 100% respectively, by what percentage does the volume of the cone increase?
The volume of a cone is given by the formula (1/3)πr²h, where r is the radius and h is the height. If the radius and height are increased by 200% and 100% respectively, the new radius is 3 times the original radius and the new height is 2 times the original height. Therefore, the new volume is (1/3)π(3r)²(2h) = (1/3)π(9r²)(2h) = 6πr²h, which is 6 times the original volume. So the volume increases by 500%.