There are two ways to do this. You could use your calculator to find out the decimal numbers that are equivalent to the two given fractions. Then check which one of the givens falls between these two numbers. I wouldn't do it that way -- not when you are told that the answer has 56 as the denominator. So ...
The best way to do it is to change the two givens so that they have a denominator of 56
The two curves intersect at two points, (0, 0) and (8, 8):
The area of a semicircle with diameter is . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of between 0 and 8. Over this interval, and , so the volume of this solid is given by the integral