Which has a greater effect on the volume? Changing the radius by a given amount or changing the height by the same amount?

Changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount. This is because the value of the radius is squared in the formula.

For my PLATO fam

doubling the radius will have a greater effect

v of cylinder=pi x square of radius x hieght

lets take an example, r=2, h=2

v=8pi

doubling the hieght, h=4

v=16pi ie twice the initial volume

doubling the radius, r=4

v=pi x 16 x 2

=32 pi ie four times the initial volume

therefore radius makes a bigger difference