Question

Curved surface area of a hollow cylinder is $4224\pi c{m}^2$. A rectangular sheet having width $33cm$ is formed cutting it along its height. Find perimeter of sheet.

Answer 1

Let cylinder has height h and radius $r$.

If cylinder is being converted to rectangle then length of the rectangle will be equal to the circumference of the base of cylinder and breath of the rectangle will be equal to height of the cylinder.

$\Rightarrow$ Sheet has length $=2\pi r$, width $=h$

Let $A$ be the C.S.A of cylinder

$A=2\pi rh=4224\pi$

$\Rightarrow 2\left(33\right)h=4224$

$\Rightarrow h=64cm$

Let $p$ be the Perimeter of rectangle

$p=2(l+w)=2(64+33)=97\times 2=194cm$.