A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
Mensuration
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Question

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.

KnowledgeBoat · Accepted Answer

Given, Each person must have 16 m³ of air to breathe. ∴ 77 persons need 77 × 16 m³ = 1232 m³. Radius of tent (r) = 7 m. Let height of conical tent be h meters. Since, conical tent needs to accommodate 77 persons, so its volume will be equal to volume of air required for 77 persons. By formula, ⇒ l² = r² + h² ⇒ l² = 7² + 24² ⇒ l² = 49 + 576 ⇒ l² = 625 ⇒ l = = 25 m. Curved surface area of tent = πrl = = 22 × 25 = 550 m². Hence, height of tent = 24 m and curved surface area of tent = 550 m².

Mathematics

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.

Mensuration

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Mathematics

A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.

Mensuration

Related Questions

A certain number of metallic cones, each of radius 2 cm and height 3 cm, are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.