Question

The radius of the base of a right circular cylinder is increased by 75% and the height is
decreased by 50%. Find the per cent increase or decrease in the volume​

Answer 1

Answer:

The increase in volume is 53.125%.

Step-by-step explanation:

If the radius of the base of a right circular cylinder is 'r' units and the height of the cylinder is 'h' units.

Then , the volume of the right circular cylinder will be πr²h cubic units.

If the radius of the base increases 75% then it will become 175r/100 units.

I.e. it will become 7r/4 units.

If the height of the cylinder decreases 50% then it will become h/2 units.

Now , the new volume will be π( 7r/4 )²(h/2) = ( 49/32 )πr²h cubic units.

Then , the increase in volume is  ( 49/32 - 1 )πr²h = ( 17/32 )πr²h cubic units.

∴ The percentage increase is [ ( 17/32 )πr²h ]/ [ πr²h ] ×100 = 53.125%.