A right circular cylinder just encloses a sphere of radius r as shown in Fig 13.1. The surface area of the sphere is equal to the curved surface area of the cylinder. Is the given statement true or false and justify your answer.
Solution:
Given, a right circular cylinder encloses a sphere of radius r
The surface area of the sphere is equal to the curved surface area of the cylinder.
We have to determine if the given statement is true or false
Radius of the sphere = radius of the cylinder = r
Height of the cylinder = diameter of sphere = 2r
Surface area of sphere = 4πr²
Where, r is the radius of the sphere
Curved surface area of the cylinder = 2πrh
Where, r is the radius of the cylinder
h = height of the cylinder
Now, curved surface area = 2πr(2r)
= 4πr²
= surface area of sphere
Therefore, the given statement is true.
✦ Try This: A right circular cylinder just encloses a sphere of radius 2r. Find the surface area of the sphere. Write True or False and justify your answer.
Given, a right circular cylinder encloses a sphere
Radius of the sphere = 2r
We have to determine the surface area of the sphere
Surface area of sphere = 4πr²
Where, r is the radius of the sphere
Surface area = 4π(2r)²
= 4π(4r²)
= 16πr²
Therefore, the surface area of the sphere is 16πr² square units.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13
NCERT Exemplar Class 9 Maths Exercise 13.2 Sample Problem 1
A right circular cylinder just encloses a sphere of radius r as shown in Fig 13.1. The surface area of the sphere is equal to the curved surface area of the cylinder. Is the given statement true or false and justify your answer.
Summary:
The given statement “A right circular cylinder just encloses a sphere of radius r as shown in Fig 13.1. The surface area of the sphere is equal to the curved surface area of the cylinder” is true
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