Question

A conical tent is to accommodate 12 persons. Each person must have 5 m? of the space on the ground and 20 m' of air to breathe. The height of the tent should be:

• A. 12 m
• B. 13 m
• C. 12.5 m
• D. 22 m

Answer 1

Answer:

A. 12 m

We need to satisfy two conditions for the conical tent:

Ground area condition

Each person needs 5 m²
For 12 persons:
$\text{Base area} = 12 \times 5 = 60 \text{ m}^2$

For a cone:
$\pi r^2 = 60$

Air (volume) condition

Each person needs 20 m³
For 12 persons:

$\text{Volume} = 12 \times 20 = 240 \text{ m}^3$

For a cone:
$\text{Volume} = \frac{1}{3}\pi r^2 h$

Substitute (\pi r^2 = 60) into volume:

$\frac{1}{3} \times 60 \times h = 240$

20h = 240

h = 12

Final Answer:

Height of the tent = 12 m