If the radius of a cylinder is doubled and height is halved, the volume will be doubled. Is the given statement true or false and justify your answer.

Solution:

Given, if the radius of a cylinder is doubled and height is halved, the volume will be doubled.

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

Volume of cylinder = πr²h

Where, r is the radius of the cylinder

h is the height of the cylinder

Given, r = 2r

h = h/2

So, volume = π(2r)²(h/2)

= π(4r²)(h/2)

= π(2r²)h

= 2πr²h

= 2(volume of cylinder)

Therefore, the given statement is true.

✦ Try This: If the length of a diagonal of a cube is 8√3 cm, then its surface area is

Given, the length of a diagonal of a cube is 8√3 cm

We have to find the surface area of the cube.

Diagonal of the cube = a√3

Where, a is the length of the side of the cube

Given, a√3 = 8√3

a = 8 cm

Surface area of cube = 6a²

= 6(8)²

= 6(64)

= 384 cm²

Therefore, the surface area of the cube is 384 cm².

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

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NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 10

If the radius of a cylinder is doubled and height is halved, the volume will be doubled. Is the given statement true or false and justify your answer.

Summary:

The given statement “If the radius of a cylinder is doubled and height is halved, the volume will be doubled” is true

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