Question 890940
Volume of a cylinder is equal to pi * r^2 * h.
r is the radius.
h is the height.


let the radius of the smaller cylinder be equal to x.
let the radius of the larger cylinder be equal to 10.
let the height of both cylinders be equal to 12.


the formulas become:


Volume of the smaller cylinder = V1 = pi * x^2 * 12
Volume of the larger cylinder = V2 = pi * 10^2 * 12


simplify both these equations as much as you can to get:


V1 = 12 * pi * x^2
V2 = 1200 * pi


the volume in between the smaller cylinder and the larger cylinder will be equal to V2 minus V1.


you get V2 - V = 1200 * pi - 12 * pi * x^2


This can be written as:


V2-V1 = 1200pi - 12pix^2


you could factor out 12pi if you wanted to, but I don't think it's necessary.


You would get:


V2-V1 = 12pi(100-x^2)