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# 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

**☛ Related Questions:**

- An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube . . . .
- The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter a . . . .
- If the radius of a right circular cone is halved and height is doubled, the volume will remain uncha . . . .

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