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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