# How Much Volume will be Change? If

If the radius of a cylinder is decreased by 50% and the height is increased by 50% then the change in volume is

- 52.5%
- 67.5%
- 57.5%
- 62.5%

**Answer: (4) 62.5% **

**Explanation:-**

**Formula-**

The volume of cylinder = Pai r^{2}h

According to the question,

Now, the volume of the cylinder = Pai(r/2)^{2} (h + h/2)

= Pai r^{2}/4 (3h/2)

= Pai r^{2}3h/8

Change volume = Pai r^{2}h – Pai r^{2}3h/8

= Pai (8r^{2}h – 3r^{2}h)/8

= Pai 5r^{2}h/8

Change in percent = (Pai 5r^{2}h/8) x 100/Pai r^{2}h

= 5 x 100/8

= 62.5%

Hence, the answer is (4) 62.5%.