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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. - ICSE Class 10 - Mathematics

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ConceptHeights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

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.

Solution

Let h be the height and r be the radius of the base of the conical tent.

According to the given information

`77xx16 = 1/3 pir^2h`

`=> 77xx16=1/3 xx 22/7 xx7xx7xxh`

`=> 77xx 16 = 1/3 xx 22xx7 xx h`

`=> h = (77xx16xx3)/(22xx7) => h = 24`m

Now, `I^2 = r^2 + h^2`

`=> I^2= 7^2 + 24^2 = 625`

`=> I = 25`

∴ Curved surface area = `pirl = 22/7 xx 7 xx 25 = 550 m^2`

Hence, the height of the tent is 24 m and the curved surface area of the tent is 550 m2

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Solution 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. Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables.
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