Question

If the height of a cone is doubled then its volume is increased by

• A. 400%
• B. 300%
• C. 200%
• D. 100%

Answer 1

Answer: (D)

100%

Let the radius of the cone is r and volume is h then

Volume of the cone$=\frac{1}{3}\pi r^{2}h$

if the height of the cone is double the

New volume$=\frac{1}{3}\pi r^2\left(2h\right)=\frac{2}{3}\pi r^{2}h$

increment of the volume$=\frac{2}{3}\pi r^{2}h-\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^{2}h$

% increase$=\frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}\times 100=100$%