Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m²
(Use π = 22/7).

Answer 1

Given:

Height of the tent h = 77 dm = 7.7 m, diameter of cylinder

Height of the cylinder h₁ = 44 dm = 4.4 m, height of cone h₂ = 33 dm = 3.3 m

We have the following diagram

Radius

The curved area of cylinder is given by

$$\begin{gathered} S_1=2\mathrm{\pi rh}=2\times \frac{22}{7}\times 18\times 4.4 \\ =497.82{\mathrm{m}}^2 \end{gathered}$$

The slant height of the cone is

$$\begin{gathered} l=\sqrt{h^2+r^2} \\ =\sqrt{3.3^2+{18}^2} \\ =\sqrt{334.89} \\ =18.3m \end{gathered}$$

The curved area of the cone is given by
$$\begin{gathered} S_2=\mathrm{\pi rl}=\frac{22}{7}\times 18\times 18.3 \\ =1035.25{\mathrm{m}}^2 \end{gathered}$$

The total area of the canvas required is given as

S = S₁ + S₂
= 497.82 + 1035.25
=1533.07 m²

Therefore the cost of the canvas at the rate of Rs 3.5 per square meter is given by

$$\begin{gathered} 1533.07\times 3.5 \\ =Rs5365.745 \end{gathered}$$

Hence the cost of the canvas is Rs 5365.745