Question

The volume of a cylinder whose radius $\text{r}$ is equal to its height is

• A. $\frac{1}{4}\mathrm{\pi }{\text{r}}^3$
• B. $\frac{{\mathrm{\pi r}}^3}{32}$
• C. ${\text{πr}}^3$
• D. $\frac{{\mathrm{\pi r}}^3}{8}$

Answer 1

The correct option is C

${\text{πr}}^3$

Explanation for the correct option:

Volume of cylinder:

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

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

And here it is given that $\text{r=h}$ so we get ,

Volume of the cylinder $=\mathrm{\pi }{\text{r}}^2{\text{(r)=πr}}^3$

Hence option(C) is the correct answer