(solved)Question 16 SSC-CGL 2020 March 4 Shift 1

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

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

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

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