If the height of a right circular cone is increased by 200%

If the height of a right circular cone is increased by 200%, and the radius of the base is reduced by 50%, then the volume of the cone

  1. remains unaltered
  2. decreases by 25%
  3. increases by 50%
  4. increases by 25%

Answer

Volume of a cone of radius r and height h, is given by 1/3 πr2h = v (say).

Now, new height = h(1 + 200/100) = h(1 + 2) = 3h

and new radius = r(1 - 50/100) = r(1 - 1/2) = r/2

So, new volume  = 1/3 π (r/2)2(3h)

= 3/4 × (1/3 πr2h) 

= 3/4 × v = 0.75v

So, Reduction in volume = (v - 0.75v)/v 

= 0.25 times = 25%

The correct option is B.