Question

The volume of a cylinder that exactly fits in a cube of side $\text{a}$ is $\_\_\_$

Answer 1

We know that volume of the cylinder $=\text{base area×height}={\text{πr}}^2\text{h}$ $\text{cubic unit}$

Where $\text{r}$ is the radius and $\text{h}$is the height of the cylinder.

When the cylinder exactly fits on the cube side $\text{a}$ the height equals to the edges of the cube and the radius equals half of the edge of the cube.

It means $\text{h=a}$$\text{,r=}\frac{a}{2}$

If we put the values of $\text{h}$ and $\text{r}$ then we get,

The volume of the cylinder $=\mathrm{\pi }{\left(\frac{\text{a}}{2}\right)}^2\mathrm{h}$$=\mathrm{\pi }\frac{{\mathrm{a}}^2}{4}\mathrm{h}=\frac{{\mathrm{\pi a}}^2\mathrm{h}}{4}\mathrm{cubic}\mathrm{units}$.

Hence, the volume is $=\frac{{\mathrm{\pi a}}^2\mathrm{h}}{4}\mathrm{cubic}\mathrm{units}$.