Question
If the radius of the base and the height of a right
circular cone are increased by 10%, what is the approximate percentage increase in volume?Solution
Let the radius of the cone = x cm Height of the cone = y cm Volume of the cone = 1/3π r2h = 1/3πx2y After increment, Radius of the cone = 1.1x cm Height of the cone = 1.1y cm Volume of the cone = 1/3π × 1.1x × 1.1x × 1.1y = 1/3 π × 1.331x2 y Difference = 1/3 π × 1.331x2y - 1/3πx2y = 1/3π × 0.331x2y Required percentage = 1/3π × 0.331x2y/(1/3π × x2y) × 100 = 33.1%
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