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

Given diameter of cylinder = 24m

Radius`(r)=24/2=12m`

Given height of cylindrical part(h₁) = 11m

∴ Height of cone part(h₂) = 5m

Vertex of cone above ground = 11 + 5 = 16m

Curved surface area of cone(S₁)= πrl

`=22/7xx12xxl`

Let l be slant height of cone

⇒ `l=sqrt(r^2+h_2^2)`

⇒ `l=sqrt(12^2+5^2`

l = 13m

∴ Curved surface area of cone `(5)=22/7xx12xx13m^2`    ...........(1)

Curved surface area of cylinder(S₂) = 2πrh

S₂ = 2π(12)(11)m²             ..........(2)

To find area of canvas required for tent

S = S₁ + S₂ = (1) + (2)

`S=22/7xx12xx13+2pi(12)(11)`

S = 490 + 829.38

S = 1320m²

∴Total canvas required for tent(S) = 1320m²