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.

Explanation

Radius of the cylinder, R = 12m and its height, H = 11m
Area of the curved surface of the cylindrical portion
`= 2pi RH` sq units
`= (2pi xx 12 xx 11) m^(2) = (264pi) m^(2)`
Radius of the cone, r = 12m
and its height, `h = (16 - 11)m = 5m`
Slant height of the cone, `l = sqrt(r^(2) + h^(2))`
`:. l = sqrt((12)^(2) + (5)^(2)) = sqrt(169) = 13m`
Area of curved surface of the cone
`= (pi rl)` sq units
`= (pi xx 12 xx 13) m^(2) = (156pi) m^(2)`
Area of canvas = (curved surface area of the cylindrical part) + (curved surface area of the concial part)
`= (264pi + 156 pi) m^(2) = (420pi) m^(2)`
`= (420 xx (22)/(7)) m^(2) = 1320 m^(2)`
Hence, the area of canvas requires is `1320 m^(2)`