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The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Is the given statement true or false and justify your answer.

Solution:

Given, the volume of the sphere is equal to two-third of the volume of a cylinder

The height and diameter are equal to the diameter of the sphere.

We have to determine if the given statement is true or false.

Let the radius and height of the sphere be r

Volume of the sphere = 4/3 πr³

Where, r is the radius of the sphere

Now, radius of cylinder = r

Height of cylinder = 2r

Volume of the cylinder = 1/3 πr²h

= 1/3 πr²(2r)

= 2/3 πr³

Therefore, the given statement is false.

✦ Try This: The volume of a sphere is equal to twice of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Write True or False and justify your answer.

Given, the volume of the sphere is equal to two-third of the volume of a cylinder

The height and diameter are equal to the diameter of the sphere.

We have to determine if the given statement is true or false.

Let the radius and height of the sphere be r

Volume of the sphere = 4/3 πr³

Where, r is the radius of the sphere

Now, radius of cylinder = r

Height of cylinder = 2r

Volume of the cylinder = 1/3 πr²h

= 1/3 πr²(2r)

= 2/3 πr³

Volume of sphere = 2(volume of cylinder)

Therefore, the given statement is true.

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

NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 1

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Is the given statement true or false and justify your answer.

Summary:

The given statement “The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere” is true

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