Question

A rectangular piece of tin of size $30cm\times 18cm$ is rolled in two ways, once along its length ($30cm$) and once along its breadth. Find the ratio of volumes of two cylinders so formed.

Answer 1

When rolled along length:

$h=18$

$\Rightarrow 2\pi r=30\Rightarrow r=\frac{15}{\pi }$

$\Rightarrow V=\pi r^{2}h=\pi (\frac{15}{\pi }{)}^2\times 18$

When rolled along breadth:

$h=30$

$\Rightarrow 2\pi r=18\Rightarrow r=\frac{9}{\pi }$

$\Rightarrow V=\pi r^{2}h=\pi (\frac{9}{\pi }{)}^2\times 30$

Therefore, Ratio of volumes$=\frac{\pi \times (\frac{15}{{\pi }^2}{)}^2\times 18}{\pi (\frac{9}{\pi }{)}^2\times 30}$

On simplifying we get,

$\Rightarrow$Ratio of volumes$=\frac{5}{3}$