A conical tent has to be accommodate 30 persons. Each person must have 5 $$m^2$$ spaces on the ground and $$120 m^3$$ of air to breather. Find the height (in m) of the tent.​

Correct option is D

​Given:

Total number of Persons = 30 

Each Persons requires space = 5 m² 

Each Persons requires air = 120 m³ 

Concept Used: ​

Volume of the Cone = Total number of Persons  $$\times$$ volume of air 

Formula Used: 

Area of the circle = $$\pi r^2$$​​

Volume of the Cone = $$\frac 13 \pi r^2 h$$ 

where, r = radius and h = height 

Solution:  

Area of the space = $$\pi r^2$$ 

$$30 \times 5 = \pi r^2 \\ \ \\ r^2 = \frac{150}{\pi}$$ 

Now, 

​$$\frac{1}{3}\pi r^2 h = 30 \times 120 \\ \ \\ \frac{1}{3}\times\pi \times\frac{150}{\pi} \times h = 30 \times 120 \\ \ \\ \ h = \frac{30 \times 120\times 3}{ 150}\\ \ \\ h = 72$$ 

Thus, the height(h) of the cone = 72 m 

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