5 persons live in a tent. If each person requires 16 m² of floor area and 100 m³ space for air then the height of the cone of smallest size to accommodate these persons would be?

Solution (By Examveda Team)

Let the height of cone h metre
⇒ Total area of ground will be required = 5 × 16 m² = 80 m²
⇒ Total volume of air is needed = 100 × 5 m³ = 500 m³
According to the question
⇒ Volume of cone = 500 m³
⇒ $$\frac{1}{3}$$ × area of ground × height = 500
⇒ $$\frac{1}{3}$$ × πr² × h = 500
⇒ $$\frac{1}{3}$$ × 80 × h = 500
⇒ Height = $$\frac{{500 \times 3}}{{80}}$$
⇒ Height of cone = 18.75 metres