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The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by. ?
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- 30%
- 31%
- 32.25%
- 34.75%
- 30%
Correct Option: C
Let the fixed height of a right circular cone is h and initial radius is r
Then, initial volume of cone, V1 = (1/3)πr2h
After increasing 15% radius of a cone = (r + 3r/20) = 23r/20
New volume become, V2 = (1/3)π(23/20)2r2h
∴ Increasing percentage = [(V2 - V1) / V1] x 100
= {[(1/3)πr2h] / [(1/3)πr2h]} {(23/20)2 - 1} x 100
= (23/20 + 1)(23/20 - 1) x 100
= 43/20 x 3/20 x 100 = 32.25%
