SarkariPYQ

SSC CGL 2022 PYQ — Question 75

SSC CGL - 21 April 2022 - Shift 3 • Quantitative Aptitude • Q75

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A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and lower circular ends of the frustum are 21m and 39m, respectively, then find the area of the cloth (in m2) used to make the tent(ignoring the wastage).

(Use  π = 227\frac{22}{7})

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 210727\frac{2}{7}

Height of the tent = 22.5m

Upper and lower radius of the frustum

R = 39/2 = 19.5, r = 21/2 = 10.5

Radius of hemisphere = 21/2 = 10.5

Height of the frustum = 22.5 - 21/2 = 12m

Slant height of the frustum = h2+(R−r)2\sqrt{h^2+(R-r)^2}

l = 122+(19.5−10.5)2\sqrt{12^2+(19.5-10.5)^2}

l = 15

TSA of tent = CSA of frustum + CSA of hemisphere

= πl(R + r) + 2πr2

= π × 15 (38/2) + (21/2) + 2π(21/2)2

=  22/7 × {450 + (441/2)}

= (22/7) × 1341/2

=  210727\frac{2}{7} m2

The area of the cloth =  210727\frac{2}{7} m2