Q. 94.2( 17 Votes )

# There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18m, find the volume of the tent.

Answer :

Given that, the tent is conical in shape.

If 1 person occupies area inside the tent = 4 m^{2}

Then 25 people will occupy area inside the tent = 25 × 4 = 100 m^{2}

⇒ Base area of the cone = 100 m^{2} …(i)

Also, base area of the cone is given by,

Base area of the cone = πr^{2}

⇒ 100 = πr^{2} [from (i)]

⇒

⇒

⇒ r^{2} = 31.82 …(ii)

⇒ r = 5.64

We have, radius of the base of the cone (r) = 5.64 m

Height of the conical tent (h) = 18 m

Now we need to find volume of this conical tent. The formula is:

Volume = πr^{2}h/3

Substituting values, we get

Volume = (3.14 × 31.82 × 18)/3 [from (ii)]

⇒ Volume = 599.5

⇒ Volume ≈ 600 m^{3}

Thus, we can say volume of the conical tent is approximately 600 m^{3}.

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