Question

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

Answer 1

Let the radius of base of the original cylinder = r
And the height of the cylinder = h
Volume of original cylinder = π r² h
Given that, the radius of new cylinder = 2r

And height= `"h"/(2)`

∴ Volume of new cylinder

= `π xx (2"r")^2 xx "h"/(2)`
= 2 x r²h
Ratio of volume of new cylinder to that of original cylinder

= `(2pi"r"^2"h")/(pi"r"^2"h")`
= 2 : 1.