The radius of a cone is raised by 20%, while the height is reduced by 10%. What is the percentage change in the volume of the cone?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 29.6% increase.
Original volume V = (1/3)πr2h
New radius = 1.2r
New height = 0.9h
New volume = (1/3)π × (1.2r)2 × 0.9h
= (1/3)π × (1.44r2) × 0.9h
= 1.296 × (1/3)πr2h
= 1.296V
Increase = 1.296V - V = 0.296V
Increase percentage = (0.296V/V) × 100 = 29.6%