Question

If the height of cylinder becomes $4$ times of original height and radius is doubled, then which of following will be true?

• A. Volume of the cylinder will be $16$ times.
• B. volume of cylinder remain unchanged.
• C. Volume of cylinder will be halved.
• D. Volume of cylinder will be $\frac{1}{4}$ of original volume.

Answer 1

The correct option is A Volume of the cylinder will be $16$ times.

Let radius of the base of cylinder be $r_1$ and let its height be $h_1$.

$\therefore$ Volume of original cylinder $\left(V_1\right)=\pi r^{2}h$ ...(1)

Now, new radius$=2r$ and new height$=4h$

$\therefore$ New volume $\left(V_2\right)=\pi (2r{)}^2\times 4h$

$\therefore V_2=16\pi r^{2}h$ ....(2)

$\therefore V_2=16V_1$

So, option A is correct.