If the radius of a sphere is increased by 11%, then what is the percentage (correct to two decimal places) increase in its volume?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 36.76%.
Volume of sphere (V) = (4/3)πr3
New radius (R) = 1.11r
New volume = (4/3)π(R)3 = (4/3)π(1.11r)3 = (4/3)πr3 × 1.367631 = 1.367631V
Increase = (1.367631V - V) = 0.367631V
Percentage increase = (0.367631V)/V × 100 ≈ 36.76%