Question

Question 8
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 33 cm. Find the perimeter of rectangular sheet?

Answer 1

Given Lateral surface area of hollow cylinder =$4224c{m}^2$
And Height of hollow cylinder = 33 cm
Curved surface area of hollow cylinder = 2$\pi$rh
$\Rightarrow 4224=2\times \frac{22}{7}\times r\times 33\Rightarrow r=\frac{4224\times 7}{2\times 22\times 33}=\frac{64\times 7}{22}cm$
Now Length of rectangular sheet = 2$\pi$r
$\Rightarrow l=2\times \frac{22}{7}\times \frac{64\times 7}{22}=128cm$
Perimeter of rectangular sheet = 2(l+b)
= 2 (128 + 33) = 2 $\times$ 161 = 322 cm
Hence perimeter of rectangular sheet is 322 cm.