Question

the radius of the base of a right circular cylinder is halved and height is doubled. what is the ratio of the volume of the new cylinder to that of the original cylinder?

Answer 1

Answer:

Let,

Height of the right circular cylinder =H

Radius of the base of the cylinder =R

Therefore,

Volume of the cylinder, V=π R 2H

Now,

New height of the right circular cylinder H′=2HNew radius of the base of the cylinder R ′= 2

Therefore,

New volume of the cylinder, V′ = π R ′2H ′= π 4R 22H

Therefore

Required ratio = V V′= πR 2Hπ 4R 22 h= 1 2=1:2 Therefore, the ratio of the volume of the new cylinder to that of the origional cylinder is 2:1.