If the radius of a sphere is increased by 20%, then find the percentage increase in its volume.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 72.8%
Let the original radius be r.
So, the new radius after a 20% increase is 1.2r.
Original volume, V1 = (4/3)πr³
New volume, V2 = (4/3)π(1.2r)³ = 1.728(4/3)πr³
Increase in volume = V2 - V1 = 0.728(4/3)πr³
Percentage increase = (Increase in volume / Original volume) × 100 = (0.728(4/3)πr³ / (4/3)πr³) × 100 = 72.8%
Therefore, the volume increases by 72.8%.