Write whether True or False and justify your answer

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

Let radius of cylinder = r

Let height of cylinder = h

Then, volume of cylinder is given by

V = πr²h …(i)

According to the question, now

Radius of the cylinder = 2r

Height of the cylinder = h/2

Then, volume of cylinder is given by

V’ = π(2r)²(h/2) = 4πr²(h/2) = 2πr²h = 2 (πr²h) = 2V

⇒ V’ = 2V

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

Hence, it is true.