A right circular cone has base radius r and height h. If the radius decreases by 20% and the height increases by 10%, what is the percentage change in volume?

Correct answer: 29.6% decrease. Volume depends on r² × h: new volume = 0.8² × 1.1 = 0.704 of the old, a 29.6% decrease.

Background: The volume of a cone is V = (1/3)πr²h.

• 10% decrease: 10% ignores the effect of squaring the radius.
• 12% decrease: 12% ignores the effect of squaring the radius.
• 18.4% decrease: 18.4% is not the product 0.64 × 1.1.

Did you know? A 20% radius decrease cuts the base area by 36%.

Memory trick: Radius is squared: 0.8² = 0.64.