# Homework Help: Sphere Question

1. Jul 14, 2010

### DanialD

1. The problem statement, all variables and given/known data

Given that the surface ares of a sphere is 36(pi)x^2+24(pi)x+12(pi) , state the volume of a cylinder that would exactly contain the sphere. (note that the height of the cylinder is twice the radius of the sphere).

2. Relevant equations

Sphere SA= 4(pi)r^2

VolCylinder= (pi)r^2h

3. The attempt at a solution

i tried to factor the function to figure out x, but its not factorable. Someone please help...

2. Jul 15, 2010

### Mentallic

Isn't it? The quadratic formula usually helps in this case.

3. Jul 15, 2010

### HallsofIvy

You can't "figure out x"- x is a variable and the final answer should depend on x. Instead, find r in terms of x. The radius of the cylinder must be the same as the radius of the sphere and the height of the cylinder must be the same as the diameter of the sphere.

4. Jul 17, 2010

### hunt_mat

Surface area is given as:
$$A=36\pi x^{2}+24\pi x+12\pi =4\pi r^{2}$$
Hence
$$r^{2}=9x^{2}+6x+3$$
You know the volume of the cylinder, so...