A conical

A conical tent can accommodate 11 people. Each person needs 4 m² of space on the ground and 20 m³ of air to breathe. Find the height of the tent.

Correct answer:

h =  15 m

Step-by-step explanation:

$$\begin{gathered} n=11 \\ {S}_1=4{\text{m}}^2 \\ {V}_1=20{\text{m}}^3 \\ S=n\cdot S_1=11\cdot 4=44{\text{m}}^2 \\ V=n\cdot V_1=11\cdot 20=220{\text{m}}^3 \\ S=\pi \cdot r^2 \\ r=\sqrt{S/\pi }=\sqrt{44/3.1416}\doteq 3.7424\text{m} \\ V=\frac{1}{3}\cdot S\cdot h \\ h=\frac{3\cdot V}{S}=\frac{3\cdot 220}{44}=15\text{m} \end{gathered}$$

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