A conical tent is to accommodate 11 person Each person must have 4m2of the space on the ground and 20m3of - Maths - Surface Areas and Volumes

Question

A conical tent is to accommodate 11 person Each person must have
4m2of the space on the ground and 20m3of air
to breath Find the height of the cone

Santosh Kumar · Accepted Answer

Let the radius of the conical text be r and height be h.

Space on the ground in the tent = πr²

$\Rightarrow 11 \times 4 = π r^{2} \Rightarrow \frac{22}{7} \times r^{2} = 4 \times 11 \Rightarrow r^{2} = \frac{7 \times 4 \times 11}{22} ... (1)$

Volume of tent = Air needed for breathing

$\Rightarrow 11 \times 20 = \frac{1}{3} π r^{2} h \Rightarrow \frac{1}{3} π r^{2} h = 20 \times 11 \Rightarrow h = \frac{11 \times 20 \times 3}{π r^{2}} \Rightarrow h = \frac{20 \times 3 \times 11}{\frac{22}{7} \times \frac{7 \times 4}{22} \times 11}$

[From equation (1)]

$\Rightarrow h = \frac{20 \times 3}{4} h = 15 m$

A conical tent is to accommodate 11 person.Each person must have 4m2of the space on the ground and 20m3of air to breath.Find the height of the cone.

A conical tent is to accommodate 11 person.Each person must have 4m²of the space on the ground and 20m³of air to breath.Find the height of the cone.