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

**Solution:**

Given, area of cloth is 165 m²

Cloth is shaped into the form of a conical tent

The radius of tent is 5 m

We have to find the volume of the conical tent.

Area of cloth = curved surface area of tent

Curved surface area of cone = πrl

Where, r is the radius of the cone

l is the slant height of the cone

Given, r = 5 m

π(5)l = 165

(22/7)l = 165/5

(22/7)l = 33

l = 33(7)/22

l = 3(7)/2

l = 21/2

l = 10.5 m

We know, l² = r² + h²

(10.5)² = (5)² + h²

110.25 = 25 + h²

h² = 110.25 - 25

h² = 85.25

Taking square root,

h = 9.23 m

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

= 1/3 (22/7)(5)²(9.23)

= 22(25)(9.23)/21

= 5076.5/21

= 241.74 m³

Therefore, the volume of the conical tent is 241.74 m³.

**✦ Try This: **A cloth having an area of 175 m² is shaped into the form of a conical tent of radius 7 m. Find the volume of the cone.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 13

**NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 3(ii)**

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

**Summary:**

A cloth having an area of 165 m² is shaped into the form of a conical tent of radius 5 m. The volume of the cone is 241.74 m³

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