SOLUTION: A diagram shows two cylinders with bases that have the same canter and heights of 12 millimeters. Also having a radius for the larger cylinder as 10 millimeters. Write an equation

Algebra ->  Volume -> SOLUTION: A diagram shows two cylinders with bases that have the same canter and heights of 12 millimeters. Also having a radius for the larger cylinder as 10 millimeters. Write an equation       Log On


   

Question 890940: A diagram shows two cylinders with bases that have the same canter and heights of 12 millimeters. Also having a radius for the larger cylinder as 10 millimeters. Write an equation that describes the volume, V, that is inside the larger cylinder but outside the one with the smaller radius r?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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)