Question

If the radius of a cylinder increases by $y$ cm, its volume becomes $V$ $c{m}^3$ . If its height increased by $4y$ cm, its volume would become $V$ $c{m}^3$. If its radius as well as its height equals $6$ cm, then find $y$.

• A. $10$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is B $12$

Volume of a cylinder or radius $r$ and height $h$ is $\pi r^{2}h$
Given, $\pi {(r+y)}^{2}h=\pi r^2(h+4y)=V$
$\Rightarrow {(r+y)}^{2}h=r^2(h+4y)$
Given, for the cylinder $r=h=6$ cm
$\Rightarrow {(6+y)}^2\times 6=6^2\times (6+4y)$
$\Rightarrow 36+y^2+12y=36+24y$
$\Rightarrow y^2-12y=0$
$\Rightarrow y(y-12)=0$
$\Rightarrow y=0$ or $12$ cm