Question

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

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• A conical tent is to accommodate 11 persons

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• Each person must have 4 square meter of space on the ground and 20 cubic meter of air to breath

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$\large\underline{\red{\bf To \: Find :-}}$

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• Height of the cone

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the radius of the conical tent be "t"

• Let the height of the conical tent be "h"

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$\underline{\bold{\texttt{Area of circular base :}}}$

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Each person will take 4 sq. m of space on ground

Thus 11 person will take 11 × 4 sq. m. space

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➜ 11 × 4

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➨ 44 sq. m. ----- (1)

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$\underline{\bold{\texttt{Volume of cone :}}}$

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Each person require 20 cu. m. space in air

Thus 11 person will take 11 × 20 cu. m.

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➜ 11 × 20

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➨ 220 cu. m. ------- (2)

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$\underline{\bold{\texttt{Area of circular base :}}}$

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➠ πr²

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⟮From (1) we get Area of base = 44 sq. m.⟯

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So,

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➜ πr² = 44

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➜ $\sf r ^2 = \dfrac { 44 \times 7 } { 22 }$

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➜ r² = 14

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➨ $\sf r = \sqrt { 14 }$ ----- (3)

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• Hence the radius of conical tent is $\sf \sqrt { 14 }$ m.

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$\underline{\bold{\texttt{Volume of cone :}}}$

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➠ $\sf \dfrac { 1 } { 3 } \pi r ^2 h$

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⟮ From (2) we get volume of cone = 220 cu. m. ⟯

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So,

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$\sf \dfrac { 1 } { 3 } \pi r ^2 h = 220$ ----- (4)

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⟮ Putting r = $\sf \sqrt { 14 }$ from (3) to (4) ⟯

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➜ $\sf \dfrac { 1 } { 3 } \pi \sqrt { 14 } ^2 h = 220$

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➜ $\sf h = \dfrac { \cancel { 220} × 3 × 7 } {\cancel { 22 } × 14 }$

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➜ $\sf h = \dfrac { 10 × 3 × \cancel 7 } {\cancel { 14} }$

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➜ $\sf h = \dfrac { 10 × 3 } {2}$

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➜ $\sf h = \dfrac { 30 } {2}$

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➨ h = 15 m

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• Hence height of conical tent is 15 m

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