The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is ____.

A....

Question

The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is ____.

A. 17.1  B. 21.0  C. 33.1  D. 72.8

Accepted Answer

The volume increases by 33.1%, so the answer is C. The volume of a cone depends on both its radius (squared) and its height. When both increase by the same percentage, we cannot simply add the percentages — the compounded effect on the product of r^2 and h must be computed. A 10% increase in r multiplies r^2 by 1.1^2 = 1.21, and a 10% increase in h multiplies h by 1.1. Together the volume multiplies by 1.1^3 = 1.331, giving a 33.1% increase.