How do i solve this geometric problem? (in each diagram, line ab is tangent to center at b. find the value of x.)

Here you would use the Pythagorean theorem which is a² + b² = c²
a would be 8
b would be x
c would be (x + 2) since part of the hypotenuse is 2 and the other part is x.
Now all you have to do is plug in and solve for x:
8² + x² = (x + 2)²          remember (x + 2)² is (x + 2)(x + 2)
64 + x² = x² +4x + 4        subtract x² from both sides
64 = 4x + 4        subtract 4 from both sides
60 = 4x          divide both sides by 4
15 = x
x is 15!

Are you trying to figure out the volume?