Question

A canvas tent is in the shape of a cylinder surmounted by a conical roof. The common diameter of the cone and the cylinder is 14 m. The height of the cylindrical part is 8 m and the height of the conical roof is 4 m. Find the area of the canvas used to make the tent. 

Answer 1

Height of the cylindrical part = H = 8 m 

Height of the conical part = h = 4 m 

Diameter = 14 m ⇒ radius = r = 7 m 

Slant height of the cone = I = 

l = `sqrt(r^2 + h^2)`

l = `sqrt(7^2 + 4^2)`

l = `sqrt(65) = 8.06` m

Slant height of cone = 8.06 m 

Area of the canvas used = Curved surface area of cylinder + curved surface area of cone

= `2pirH + pirl`

= `(2 xx 22/7 xx 7 xx 8) + (22/7 xx 7 xx 8.06)`

= 352 + 177.32

= 529.32 m²

Area of the canvas used = 529.32 m²