Question

A conical tent is to accommodate 11 persons. Each person must have 4 m² of the space on the ground and 20 m³ of air to breath. Find the height of the cone.

Answer 1

Suppose that the radius of base is r m and the height is h m.
Area of base of the tent = number of people $\times$ area required by 1 person
= 11$\times$4 = 44 m²

Now, volume of the cone = number of people $\times$volume of air to breadth for 1 person
= 11$\times$20 = 220 m³

$$\begin{gathered} \therefore \mathrm{\pi }{r}^2=44 \\ \Rightarrow r^2=\frac{44\times 7}{22}=14 \end{gathered}$$

$$\begin{gathered} \mathrm{Also},\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h\mathit{}=220 \\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times 14\times h=220 \\ \Rightarrow h\mathit{}=\frac{220\times 21}{22\times 14}=15\mathrm{m} \end{gathered}$$

∴ Height of the tent = 15 m