Question

If the radius and height of a cone are both increased by 100% , then its volume is increased by:

• A. $400$%
• B. $300$%
• C. $200$%
• D. $700$%

Answer 1

Answer: (D)

$700$%

Let

old radius of cone = r

old height of cone = h

They increased by 100%

So,

new radius = 2r

new height - 2h

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

$=8\times \frac{\pi }{3}{r}^{2}h$

New volume = 8 $\times$ old volume ... (1)

change in volume =

$\frac{newvolume-oldvolume}{oldvolume}\times 100$

From (1)

change in volume $=\left(\frac{8-1}{1}\right)\times 100$

$=700\%$