Question

The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ equals to the volume of the hemisphere of radius $\text{r}$

• A. True
• B. False

Answer 1

The correct option is A True

Volume of the cone:

Edge of the cube $=2\text{r}$

Diameter of the cone $=2\text{r}$

$\Rightarrow$radius of the cone $=\frac{2\text{r}}{2}=\text{r}$

Height of the cone $\text{h}$$=$height of the cube $=2\text{r}$

We know that volume of the cone is $=\frac{1}{3}{\text{πr}}^2\text{h}$

If we put the values of $\text{h}$ in the formula we get,

$\text{V=}\frac{1}{3}{\text{πr}}^2\text{(2r)=}\frac{2}{3}{\mathrm{\pi r}}^3$$=$volume of the hemisphere

Hence the given statement is a true statement.