Question

If the volume of sphere and cone are equal with same radius$\left(r\right)$ then calculate height$\left(h\right)$ of the cone.

• A. $h=4r$
• B. $h=2r$
• C. $h=r$
• D. $h=\frac{r}{2}$

Answer 1

Answer: (A)

$h=4r$

$r$ nethe radius of both sphere and cone and let $h$ be the height of cone

Volume of sphere $=\frac{4}{3}\pi r^3$

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

It is given that

Volume of sphere $=$ volume of cone

$\Rightarrow \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi r^3$

$\Rightarrow h=4r$