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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┬а=13 cm and r2┬а= 7┬аcm

Let тАШLтАЩ be slantheight of the frustum cone

Then, we know that

Curved surface area ofthe frustum┬а(s1) = ╧А(r1┬а+ r2) ├Ч L =┬а╧А(13 + 7) ├Ч 10┬а=┬а200 ╧А m2

Then, given slantheight of conical cap = 12 m

Base radius of uppercap cone = 7 m

So, the curved surfacearea of upper cap cone┬а(s2) = ╧Аrl┬а=┬а╧А ├Ч 7 ├Ч12┬а=┬а264┬аm2

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

S =┬а200╧А + 264 =892.57 m2

Therefore, the canvasrequired for the tent is 892.57 m2.

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