Question

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.(Take π = \(\frac{22}7\))

Answer 1

Height of the frustum, h = 8 m 

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

Let l be the slant height of the frustum 

⇒ l = \(\sqrt{(r' - r")^2 + h^2}\)

⇒ l = \(\sqrt{13 - 7)^2 + 8^2}\)

⇒ l = 10 cm 

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

= π (13 + 7) × 10 

= 628.57 cm² 

Slant height of the conical cap = 12 m 

Base radius of the cap = 7 m 

Curved surface of the cap, A’’ = πrl 

= π × 7 × 12

= 264 m² 

Total canvas required = A’ + A’’ 

= 628.57 + 264 

= 892.57 m² 

∴ Total canvas = 892.57 m²