Question 1181724
<br>
There largest right circular cylinder with height 8 that can be cut from a sphere with diameter 12 is the cylinder that can be inscribed in the sphere.<br>
For that cylinder, each base is 8/2 = 4 units from the center of the sphere.  Then, from the Pythagorean Theorem, with the radius of the sphere being 6, the radius of each base of the cylinder is 2*sqrt(5).<br>
And then the volume of the cylinder is<br>
{{{V=(pi)(r^2)(h)=(pi)(20)(8)=160pi}}}<br>
ANSWER: 160pi<br>