Question

Choose the correct answer in each of the following :

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

(a) $100\%$ (b) $200\%$ (c) $300\%$ (d) $400\%$

Answer 1

ANSWER:
(a) 100 %
Suppose that the height of the cone becomes 2h and let its radius be r.
The new volume of the cone = $\frac{1}{3}\pi r^2\left(2h\right)=\frac{2}{3}\pi r^{2}h=2\times volumeofthecone$
Increase in volume = $\frac{2}{3}\pi r^{2}h-\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^{2}h$
∴ Percentage increase =$\frac{increaseinvolume}{initialvolume}$×100 %
=$\frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}$ ×100% = 100%
Hence, the volume increases by 100%.