If the radius of a right circular cone is increased by p%

If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone?

  1. p2
  2. 2p2
  3. p2/100
  4. p(2 + p/100)

Answer

Volume of cone = 1/3 × πr2h

As the height is same, volume of cone ∝ r2

Radius is increased by p%

New Radius = r(1 + p/100)

Take example and assume that p = 100% (radius is doubled)

New radius = 2r

Increase in volume = (2r)2 - r2 = 3r2

New volume of cone ∝ 3r2, which is 3 times the original volume.

Insert p = 100 in the given options, option D is equal to 3.

p(2 + p/100) = p(2 + 100/100) = 3p or 300%

The correct option is D.