If the radius of sphere is decreased by 10 percent, then volume of sphere will be decreased by what percentage ?
Answer & explanation
Correct answer: option 4
The radius of sphere is decreased by 10 percent
Original : New
Radius 10 : 9
Initial Volume = \(\frac{4}{3}\) × \(\pi \) × r × r × r
= \(\frac{4}{3}\) × \(\pi \) × 10 × 10 ×10
= \(\frac{4}{3}\) × 1000
Final Volume = \(\frac{4}{3}\) × \(\pi \) × r × r × r
= \(\frac{4}{3}\) × \(\pi \) × 9 × 9 × 9
= \(\frac{4}{3}\) × 729
Difference = \(\frac{4}{3}\) × (1000 - 729)
Required percentage = \(\frac{271}{1000}\) × 100 = 27.1%