Question

If radius of the base of a right circular cone is increased by 15% keeping the height same, the volume of the cone will increase by

• A. 30%
• B. 31%
• C. 32.25%
• D. 34.75%

Answer 1

The correct option is C

32.25%

Let the radius be x
After increase in radius, it would be 1.15 x
Now volume of new cone $=\frac{1}{3}\pi (1.15x{)}^{2}h$
Volume of old cone =$\frac{1}{3}\pi x^{2}h$
Now, increase in volume =new volume -old volume $=\frac{1}{3}\pi x^{2}h({1.15}^2-1)=0.3225\times \frac{1}{3}\pi x^{2}h$
% change in volume $=\frac{IncreaseintheVolume}{OldVolume}\times 100\%=\frac{0.3225\times \frac{1}{3}\pi x^{2}h}{\frac{1}{3}\pi x^{2}h}\times 100\%=32.25\%$