Question

A conical tent is to accommodate 10 persons. each person must have 6 meter square space to sit and 30 meter cube of air to breathe. what will be the height of the cone?

Answer 1

Answer:

15 m

Step-by-step explanation:

Area required by one person = 6 sq.m.

Area required by 10 persons = $6 \times 10 =60 m^2$

So, Area of base conical tent = 60 sq.m.

Formula of Area of base of cone  = $\pi r^2$

So, $60=3.14 \times r^2$

$\frac{60}{3.14}=r^2$

$\sqrt{\frac{60}{3.14}}=r$

$4.37=r$

Volume of cone = $\frac{1}{3} \pi r^2 h$

                          = $\frac{1}{3} \times 3.14 \times (4.37)^2 h$  

Air required by 1 person = 30 cubic m

Air required by 10 person = $30 \times 10 =300 m^3$

So, Volume of cone =  $300 m^3$

So,  $\frac{1}{3} \times 3.14 \times (4.37)^2 h=300$  

$h=15.008$  

Hence the height of the cone is approximately 15 m