Question

The radius of the base of a right circular cylinder is halved and the height is doubled. Find the ratio of the volume of the new cylinder to the volume of the original one

Answer 1

let the original radius of cylinder be r and height be h.
then volume of cylinder =πr^2h
if radius of base is halved then ,radius obtained=r/2 and height=2h.
so, new volume of cylinder= π(r/2)^2.2h
=1/2 πr^2h
change in volume= or volume- new volume
=πr^2h - 1/2 πr^2h
=πr^2h cubic units