Finding the mass?

Question

If a cylinder of 100 kg has a radius of 2 m has a smaller cylinder cut out with a radius of 1 m, what is its mass? How would I find this?

Answer 1

Mass is proportional to volume, and the volume of a cylinder is proportional to the square of the radius, because V = pi*(r^2)*h. So if you halve the radius and keep the height the same, the factor of change in the mass is (1/2)^2 = 1/4. So the mass is (100 kg)*1/4 = 25 kg.

Answer 2

You have to do the ratio of the area
3.1416 * (2m)^2 / 3.1416 (1m)^2

then 4/1 you have a ratio of 4

then 100 / 4 = 25