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Question 22 Volume And Surface Area Of Solids Exercise 15C

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5m.

Find the volume of the cone.

Answer:

A cone is a solid three-dimensional geometric object with a circular base and a pointed apex at the top. A cone is made up of one face and one vertex. For a cone, there are no edges.

The space or capacity of a cone is defined by its volume. A cone is a three-dimensional geometric object with a circular base that tapers to a point called the apex or vertex from a flat base.

We know that

Curved surface area of the tent = area of the cloth = 165 m2

So we get

Πrl = 165

By substituting the values

(22/7) × 5 × l = 165

On further calculation

l = (165 × 7)/ (22 × 5) = 21/2 m

We know that

h = √ (l2 - r2)

By substituting the values

h = √ ((21/2)2 - 52)

On further calculation

h = √ ((441/4) – 25) = √ (341/4)

So we get

h = 9.23m

We know that

Volume of the tent = 1/3 πr2h

By substituting the values

Volume of the tent = 1/3 × (22/7) × 52 × 9.23

On further calculation

**Volume of the tent = 241.7 m3**

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