The length of radius of a right circular cylinder is decreased by 50% and height is increased by 50% . Calculate how much percent of the volume will be changed.

Explanation

Let the radius of the cylinder be r units and height be h units.
`:.` the volume of the cylinder `= pi r^(2) h` cubic-units
If radius is decreased by 50% the radius becomes `( r- rxx (50)/(100)) "units" = (r-(r)/(2)) "units" = r/2` units.
Also, if height is increased by 50%, then it becomes `( h + h xx (50)/(100) ) "units" = (h + (h)/(2)) "units" = (3h)/(2) ` units.
Then the volume of the cylinder `= pi xx (r/2)^(2)xx(3h)/(2)` cubic-units `= (3 pi r^(2) h)/(8)` cubic-units
So, the volume decreases by `(pi r^(2) h - (3 pi r^(2) h)/(8))` cubic-units
`=(8 pi r^(2) - 3 pi r^(2) h)/(8) ` cubic-units `= ( 5 pi r^(2) h)/(8) ` cubic- units
So, the required percentage `= ((5 pi r^(2)h)/(8))/(pi r^(2)h)xx100 % = 5/8 xx 100% = (125)/(2) % = 62(1)/(2)%`
Hence the volume will be decreased by `62 (1)/(2) %`.