Question

9. A conical tent is
Il persons. Each person
must have 4 sq. m of space on the ground and 20 m of air
to breath. Find the height of the cone.pls​

Answer 1

Correct 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 breathe. Find the height of the cone.

Solution:

Let 'r' be the radius and 'h' be the height of cone.

• Space on the ground required by each person = 4 m².

Therefore,

Space on the ground required by 11 persons = 11 × 4 = 44 m².

Space on the ground required by 11 persons = Area of cone = 44 m²⠀ ⠀

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• Air required by each person to breathe = 20 m³

Air required by 11 persons to breathe = 11 × 20 = 220 m³

Air required by 11 persons to breathe = Volume of cone = 220 m³.

• Area of base of conical tent,

⇏ πr² = 44

⇏ 22/7 × r² = 44

⇏ r² = 44 × 7/22

⇏ r² = 14

⇏ r = √14 m

Also,

• Volume of cone = 220 m³

⇏ 1/3πr²h = 220 m³

⇏ 1/3 × 22/7 × √14 × √14 × h = 220

⇏ 1/3 × 22/7 × 14 × h = 220

⇏ 44/3 × h = 220

⇏ h = 220 × 3/44

⇏h = 15 m

∴ Hence, Height of cone is 15 m.