A conical tent has to accommodate 40 persons. Each person requires 5 $$m^2$$​ space on the ground and 70 $$m^3$$​ of air to breathe. Find the height (in m) of the tent (use π = 22/7).

Correct option is C

Given:

Number of persons = 40
Each person requires:
Ground space = 5 m²
Air to breathe = 70 m³
Use $$\pi = \frac{22}{7}$$​​
Formula Used:

The volume of a cone is given by:

​$$V = \frac{1}{3} \pi r^2 h$$​​

$$\text{Area of base} = \pi r^2$$​

Solution:
Each person requires 5 m² of ground space.
Total ground space = $$40 \times 5 = 200 \, \text{m}^2$$​​
The ground space is the area of the base of the cone.
$$\text{Area of base} = \pi r^2 = 200$$​​
$$r^2 = \frac{200}{\pi} = \frac{200}{\frac{22}{7}} = \frac{200 \times 7}{22} = \frac{1400}{22} = 63.636$$​​
$$r = \sqrt{63.636} \approx 7.98 \, \text{m}$$​​
Each person requires 70 m³ of air.
Total air volume =$$40 \times 70 = 2800 \, \text{m}^3$$​​
V = $$\frac{1}{3} \pi r^2 h$$​​
2800 =$$\frac{1}{3} \times \frac{22}{7} \times (7.98)^2 \times h$$​​

2800 =$$\frac{1}{3} \times \frac{22}{7} \times 63.68 \times h$$​

2800 =$$\frac{1}{3} \times 22 \times 9.1 \times h$$​​

2800 = $$\frac{200.2}{3} \times h$$​​
2800 =$$66.733 \times h$$​​
h = $$\frac{2800}{66.733} \approx 41.96 \, \text{m}$$​​
The height of the tent is approximately 42 meters.

Option (C) is right.