Question

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true?

• A. Total surface area of the cylinder will be doubled
• B. Total surface area of the cylinder will remain unchanged
• C. Total surface of the cylinder will be halved
• D. None of these

Answer 1

The correct option is B Total surface area of the cylinder will remain unchanged

We have,

The height of cylinder $=\frac{1}{4}$of the original height

The radius is doubled

Then,

Volume of cylinder

$=\pi r^{2}h$

$\text{Height}=\frac{1}{4}h$

$\text{Radius}=2r$

Now, Volume of cylinder

$\begin{align}

$=\pi {\left(2r\right)}^2\times \frac{1}{4}h$

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

$\Rightarrow \pi r^{2}h$

Hence, it is unchanged

This is the answer.