Question

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.

Answer 1

Diameter = 24 m 

r = \(\frac{24}2\) = 12 

Height of cylinder, H = 1cm 

Height of cone, h = 16 -11 = 5 m 

Slant height (l) = \(\sqrt{r^2 + h^2}\)

= \(\sqrt{12^2 + 5^2}\)

= \(\sqrt{169}\) = 13 m

Surface area of tent = curved surface area of cylinder + curved surface area of cone 

= 2πrH + πrl 

= 2 × (\(\frac{22}7\)) × 12 × 11 + (22/7) × 12 × 13 

= (\(\frac{22}7\)) × 12 (22 +13) 

= (\(\frac{22}7\)) × 12 × 35 

= 1320 m²