If the radius of a sphere is increased by 27%, then what will be the percentage increase (up to two decimal places) in its volume?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 104.84%.
Volume of sphere ∝ Radius3
⇒ Vi/Vf = (Ri/Rf)3
Let the initial radius of the sphere be 100.
New radius = 127% of 100 = 127
⇒ Vi/Vf = (100/127)3
⇒ Vi/Vf = (1/1.27)3
⇒ Vi/Vf = (1/2.048)
Change in volume = [(2.0484 - 1)/1] × 100
⇒ 1.0484 × 100 = 104.84%