Question

a conical tent is to accommodate 11 person. each person must have 4sq. meters of the space on the ground and 20 cubic meters of air to breath. find the height of the cone? ​

Answer 1

Step-by-step explanation:

ANSWER

Area of base = 11×4=44 m

2

πr

2

=44 m

2

Volume of the cone = 11×20=220 m

3

3

1

πr

2

h=220 m

3

Therefore,

πr

2

3

1

πr

2

h

=

44

220

3

h

=5

h=15 m

Answer 2

Answer:

let the radius of the conical tent be 'r' m and height be 'h' m.

$space \: on \: the \: ground \: required \: by \: each \: person = {4m}^{2} \\ are \: of \: base = 11 \times 4 = {44m}^{2} \\ \\ air \: requird \: by \: each \: person \: to \: breathe \: = {20}^{2} \\ volume \: of \: cone \: 11 \times 20 = {220m}^{3} \\ area \: of \: the \: base \: of \: conical \: tent \: \pi {r}^{2} = 44 \\ {r}^{2} = \frac{442 \times 7}{22} = r = \sqrt{14m} \\ \\ volume \: of \: con \: = 220 \\ \frac{1}{3} \pi {r}^{2} h = 220 \\ \frac{1}{3} \times \ \frac{22}{7} \times \sqrt{14} 2 \times h = 220 \\ h = \frac{220 \times 3 \times 7}{22 \times 14} = 15m$

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