Question

If the height of a cylinder becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ of the original height and the radius is doubled, then which of the following will be true?

• A. Volume of the cylinder will be doubled.
• B. Volume of the cylinder will remain unchanged.
• C. Volume of the cylinder will be halved.
• D. The volume of the cylinder will be$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ the original volume.

Answer 1

The correct option is B

Volume of the cylinder will remain unchanged.

Explanation for the correct option:

Find the change in the area of the cylinder.

Let the height of the cylinder be $\mathrm{h}$and the radius be $\mathrm{r}$.

The volume of the cylinder $={\mathrm{\pi r}}^2\mathrm{h}$

If the height of the cylinder be $\frac{\mathrm{h}}{4}$and the radius be $2\mathrm{r}$.

Volume after changing dimension $=\mathrm{\pi }{\left(2\mathrm{r}\right)}^2\left(\frac{\mathrm{h}}{4}\right)=\mathrm{\pi }\left(4{\mathrm{r}}^2\right)\left(\frac{\mathrm{h}}{4}\right)={\mathrm{\pi r}}^2\mathrm{h}$

The volume of the cylinder remains unchanged after changing the dimensions.

Hence option $\left(b\right)$ is the correct answer.