Question

If the height of a cylinder becomes $\frac{1}{8}$ 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. None of the above

Answer 1

The correct option is C

Volume of the cylinder will be halved

Let us assume the height and radius of the original cylinder as $h$ and $r$ respectively.

Let $V_1$ be the original volume and $V_2$ be the volume after the change in height and radius.

Therefore volume of the original cylinder is given by: $V=\pi r^{2}h$

height of a cylinder becomes $\frac{1}{8}$of the original height and the radius is doubled

$Wehave,r_2=2rand{h}_2=\frac{h}{8}$

So the new volume is given by:

$V_2=\pi r_2^2{h}_2=\pi \left(2r{)}^2\right(\frac{h}{8})$

$\Rightarrow V_2=\frac{4\pi r^{2}h}{8}$

$\Rightarrow V_2=\frac{\pi r^{2}h}{2}=\frac{V_1}{2}$

$\Rightarrow V_2=\frac{V_1}{2}$

Hence the correct answer is Option C