Finding Volume of Cylinder Containing Sphere

[DanialD]

Homework Statement

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).

Homework Equations

Sphere SA= 4(pi)r^2

VolCylinder= (pi)r^2h

The Attempt at a Solution

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

 

[Mentallic]

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

 

[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.

 

[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...