2015 · Q51
If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone
Elementary MathematicsMensuration
- Aremains unaltered
- Bdecreases by 25%
- Cincreases by 25%
- Dincreases by 50%
Explanation
This tests how volume scales with dimensions. "Increased by 200%" means the height becomes 3h, and "reduced by 50%" means the radius becomes r/2. New volume = (1/3)π(r/2)²(3h) = (3/4)(1/3)πr²h = 0.75V, a 25% decrease. The trap is option (c), from treating "increased by 200%" as doubling rather than tripling. Hence option (b).