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

Solution:

Let the radius of the base of a right circular cylinder be r and height be h.

Volume of the cylinder, V₁ = r²h

The radius of the base of a right circular cylinder is halved and the height is doubled.

So radius of new cylinder = r/2

Height of new cylinder = 2h

Volume of the new cylinder, V₂ = r²h

= (r/2)² ×2h

= ½ r²h

So ratio of volume of new cylinder to the original cylinder , V₂/V₁= ½ r²h/r²h = ½

Hence the required ratio is 1:2.