Question

A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder is __________.

Answer 1

It is given that, a rectangular tin sheet is 12 cm long and 5 cm broad. When it is rolled along its length to form a cylinder by making the opposite edges just to touch each other, then the circumference of the base of the cylinder so formed is same as the length of the rectangular sheet and the height of the cylinder is same as the breadth of the rectangular sheet.

Let r and h be the radius and height of the cylinder, respectively.

Height of the cylinder, h = 5 cm .....(1)

Also,

Circumference of base of cylinder = Length of the rectangular tin sheet = 12 cm

⇒ 2$\mathrm{\pi }$r = 12 cm

$\Rightarrow r=\frac{6}{\mathrm{\pi }}$ .....(2)

∴ Volume of the cylinder

$=\mathrm{\pi }{r}^{2}h$

$=\mathrm{\pi }\times {\left(\frac{6}{\mathrm{\pi }}\mathrm{cm}\right)}^2\times 5\mathrm{cm}$ [Using (1) and (2)]

$=\frac{180}{\mathrm{\pi }}{\mathrm{cm}}^3$

Thus, the volume of the cylinder so formed is $\frac{180}{\mathrm{\pi }}{\mathrm{cm}}^3$.

A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder is $\underline{\frac{180}{\mathrm{\pi }}{\mathrm{cm}}^3}$.