Q. 94.0( 4 Votes )

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

Answer :

Height of the frustum, h = 8m

Radii of frustum are: r’ = 13m and r’’ = 7m

Let l be the slant height of the frustum

⇒ l = 10cm

Curved surface area of frustum, A’ = π (r’ + r’’) × l

= π (13 + 7) × 10

= 628.57 cm^{2}

Slant height of the conical cap = 12m

Base radius of the cap = 7m

Curved surface of the cap, A’’ = πrl

= π × 7 × 12

= 264m^{2}

Total canvas required = A’ + A’’

= 628.57 + 264

= 892.57 m^{2}

∴ Total canvas = 892.57 m^{2}

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