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Question -

A tent consists of a frustum of a cone capped by a cone. If radii of the ends of the frustum be 13 m and 7 m, the height of frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent.



Answer -

Given,

Height of frustum (h)= 8 m

Radii of the frustumcone are 13 cm and 7 cm

So, r1 =13 cm and r2 = 7 cm

Let ‘L’ be slantheight of the frustum cone

Then, we know that

Curved surface area ofthe frustum (s1) = π(r1 + r2) × L = π(13 + 7) × 10 = 200 π m2

Then, given slantheight of conical cap = 12 m

Base radius of uppercap cone = 7 m

So, the curved surfacearea of upper cap cone (s2) = πrl = π × 7 ×12 = 264 m2

Thus, the total canvasrequired for tent (S) = s1 + s2

S = 200π + 264 =892.57 m2

Therefore, the canvasrequired for the tent is 892.57 m2.

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