Question

In Fig, you see the frame of a lampshade. It is to be covered with a decorative cloth, The frame has a base diameter of $ 20 cm$ and height of $ 30 cm.$A margin of$ 2.5 cm$ is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. (Assume $ \mathrm{\pi }=\frac{22}{7}$)

Answer 1

Given : Base diameter of the frame$=20\mathrm{cm}$

$\therefore$Base Radius of the frame $=\raisebox{1ex}{$20$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=10\mathrm{cm}$

Height of the frame (including margins provided for folding the frame over top and bottom of frame) $=30+2.5+2.5=35\mathrm{cm}$

Cloth required for covering the lampshade $=$ Curved surface area of lampshade

$$\begin{gathered} =2\mathrm{\pi rh} \\ =2\times \left(\frac{22}{7}\right)\times 10\times 35 \\ =2200{\mathrm{cm}}^2 \end{gathered}$$

Hence $2200{\mathrm{cm}}^2$cloth is required for covering the lampshade.