Question

Find the volume of largest possible cone can be curved out from hemisphere of radius 'r'.

• A. $\frac{1}{3}\pi r^3$
• B. $\frac{2}{3}\pi r^3$
• C. $\frac{1}{2}\left(volumeofhemisphere\right)$
• D. $\frac{4}{3}\pi r^3$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{1}{3}\pi r^3$
C $\frac{1}{2}\left(volumeofhemisphere\right)$

R.E.F image

for largest cone $h=r$ & $r=R$

$\Rightarrow v=\frac{\pi }{3}{r}^{2}h=\frac{\pi }{3}{r}^3$

$\Rightarrow v=\frac{1}{2}(vol.ofhemisphere)$