Question

The lateral surface area of a hollow cylinder is $4224c{m}^2$. It is cut along its height and formed a rectangular sheet of width $33cm$. Find the perimeter of rectangular sheet?

Answer 1

Given:

Lateral surface area of hollow cylinder$=4224c{m}^2$
Height of hollow cylinder $\left(h\right)=33cm$
Curved surface area of hollow cylinder $=2\pi rh$

$\Rightarrow 2\pi rh=4224c{m}^2$

$\Rightarrow 2\times \frac{22}{7}\times r\times 33cm=4224c{m}^2$

$\Rightarrow r=\frac{4224c{m}^2\times 7}{2\times 22\times 33cm}$

$\Rightarrow r=\frac{32\times 7}{11}cm$

Since, circumference of the base of cylinder becomes length of rectangular sheet

Now Length of rectangular sheet $=2\pi r$

$\Rightarrow l=2\times \frac{22}{7}\times \frac{32\times 7}{11}$

$\Rightarrow l=128cm$---(1)

Similarly, Breadth of rectangular sheet is height of cylinder.

$\Rightarrow b=33cm$ ---(2)

Perimeter of rectangular sheet $=2(l+b)$
$=2(128cm+33cm)$

$=2\times 161cm$

$=322cm$
Therefore, the perimeter of rectangular sheet is $322cm$.