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.?

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%