A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical portion is 24 m and its height is 11 m. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make the tent.

The figure of the circus tent is shown below:

Diameter of cylindrical portion = 24 m

Radius of cylindrical portion (r) = $\dfrac{\text{Diameter}}{2}$

= $\dfrac{24}{2}$ = 12 m.

Height of the cylindrical part, H = 11 m.

Since vertex of cone is 16 m above the ground, height of cone, h = 16 - 11 = 5 m.

h = 5 m.

Radius of cone = 12 m.

∴ Radius of cone is also equal to r.

Slant height of the cone, l = $\sqrt{h^2 + r^2}$.

l = $\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$ m.

Area of canvas used to make the tent = Curved surface area of the cylindrical part + Curved surface area of the cone.

Area of the canvas used to make the tent = 2πrH + πrl = πr(2H + l).

Putting values we get,

Area of the canvas = $\dfrac{22}{7} \times 12 \times (2 \times 11 + 13)$

$= \dfrac{22}{7} \times 12 \times 35 \\[1em] = 22 \times 12 \times 5 \\[1em] = 1320 \text{ m}^2$

Hence, the area of the canvas used to make the tent is 1320 m².