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.
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 cm2
Slant height of the conical cap = 12m
Base radius of the cap = 7m
Curved surface of the cap, A’’ = πrl
= π × 7 × 12
= 264m2
Total canvas required = A’ + A’’
= 628.57 + 264
= 892.57 m2
∴ Total canvas = 892.57 m2
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