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# In figure below, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of $ 20 \mathrm{~cm} $ and beight of $ 30 \mathrm{~cm} $. A margin of $ 2.5 \mathrm{~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.

"

Given:

The frame has a base diameter of \( 20 \mathrm{~cm} \) and height of \( 30 \mathrm{~cm} \). A margin of \( 2.5 \mathrm{~cm} \) is to be given for folding it over the top and bottom of the frame.

To do:

We have to find how much cloth is required for covering the lampshade.

Solution:

Diameter of the base $d=20\ cm$

Radius of the base $r =\frac{20}{2}$

$=10\ cm$

Height of the lampshade $h = 30\ cm$

A margin of $2.5\ cm$ is used for folding it over the top and bottom.

This implies,

The total height of the frame $H = 30 + 2.5 + 2.5$

$H = 35\ cm$

Therefore,

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

$=2 \pi rH$

$=2 \times \frac{22}{7} \times 10\times 35$

$=\frac{440\times35}{7}$

$=440 \times 5$

$=2200 \mathrm{~cm}^{2}$

The area of cloth required for covering the lampshade is $2200 \mathrm{~cm}^{2}$.

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