The radius of the base of a right circular cone is increased by 15%

Mensuration Percentages

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

  1. 34.75%
  2. 32.25%
  3. 31%
  4. 30%

Answer

Volume of a cone = πr2h, where r is the radius of base and h is the height of the cone.

So, let initial volume be = V1

Final volume, V2 = πR2h, where R = r(1 + 0.15) = 1.15r

So, V2 = 1.3225 πr2h

Increase in volume = (V2 - V1) /V1 × 100%

= (1.3225 πr2h - πr2h)/πr2h × 100% = 32.25%

The correct option is B.