Question

A conical tent is to accommodate $11$ persons. Each person must have $4m^2$ of the space on the ground and $20m^3$ of air to breathe. Find the height of the conical tent $[Take,\pi =\frac{22}{7}]$.

Answer 1

Let $r$ and $h$ be the radius and height of the conical tent respectively

It is given that each person needs $4m^2$ area on ground

There are total $11$ persons, therefore the total area $=44m^2$
Area of base of cone (circular base) should be equal to to the area of all persons.

$\therefore \pi \times r^2=44m^2$

Now each person require $20m^3$ volume.
Total volume required by the persons should be equal to volume of the cone.

Therefore total volume is given by

$V=\frac{1}{3}\pi \times r^2\times h=11\times 20m^2$

Substituting $\pi \times r^2$ with $44m^2$, we get

$V=\frac{1}{3}\times 44m^2\times h=220\times m^2$

$\therefore h=\frac{220\times 3}{44}=15m$