I'll try to get through as many problems as I can!
3. This is going to be a bit tricky to explain without a diagram, but just draw one yourself on a piece of paper and follow along.
Let's start off with finding the cylinder's height.
First, draw the cylinder's space diagonal. The space diagonal of the cylinder is going to be the circle's diameter, which equals 10.
Now draw the diameter of the cylinder's base. The diameter of the base, the space diagonal, and the height form a right triangle. Using the Pythagorean Theorem, we find that the height equals the square root of 102-62 , which is 8.
Now we can figure out the volume of the cylinder: 32\(\pi\)*8= 72\(\pi\)
Now we find the sphere's volume: \(\frac{4}{3}\pi\) * 53
The space inside the sphere and outside the cylinder equals the sphere's volume - the cylinder's volume, which you should be able to calculate.