Question

If radius of the base of a right circular cone is increased by 15%, then its volume 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
New radius (15% increase) = 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 $=\frac{IncreaseintheVolume}{OldVolume}\times 100\%=\frac{0.3225\times \frac{1}{3}\pi x^{2}h}{\frac{1}{3}\pi x^{2}h}\times 100\%=32.25\%$