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

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Solution

Slant height of frustum $= \sqrt{{(R_{1} - R_{2})}^{2} + H^{2}} = \sqrt{{(13 - 7)}^{2} + 8^{2}} = \sqrt{100} = 10 m$
Canvas required $=$ CSA of cone + CSA of frustum
$= π r l + π (R_{1} + R_{2}) L$
$= π [7 \times 12 + (13 + 7) \times 10] = \frac{22}{7} [84 + 200] = \frac{22}{7} \times 284 = 892.57 m^{2}$

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

Slant height of frustum =√(R1−R2)2+H2=√(13−7)2+82=√100=10mCanvas required = CSA of cone + CSA of frustum =πrl+π(R1+R2)L =π[7×12+(13+7)×10]=227[84+200]=227×284=892.57m2

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