### Question 16

SSC-CGL 2020 Mar 4 Shift 1

A conical tent of circular base with perimeter 66m and height 36m is made of canvas. Find the area of canvas required to make the tent.

### Solution in Detail

given base perimeter = $\displaystyle 66$ m

$\displaystyle \therefore 2\pi R = 66 $

$\displaystyle \therefore 2 \times \frac{22}{7} \times R = 66$

$\displaystyle \implies R = 66 \times \frac{7}{22 \times 2} $

$\displaystyle \therefore R = \frac{21}{2}$

also given $\displaystyle H = 36$ m

Slant L is needed now. We usually need to apply pythagorean theorem. But a slight presence of mind can help!

Observe $\displaystyle R = \frac{21}{2} = \frac 32 \times 7$

Also observe $\displaystyle H = 36 = \frac 32 \times 24$

But 24, 25 and 7 are pyth triplets

$\displaystyle \therefore L = \frac 32 \times 25 = \frac{75}{2}$

Curved surface area CSA

$\displaystyle = \pi \times R \times L$

$\displaystyle = \frac {22}{7} \times \frac{21}{2} \times \frac{75}{2}$

$\displaystyle = 1237.5 \text{ m}^2\:\underline{Ans}$

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