Well, you can find the cross sectional area of the two curves.
The sine curve has equation:
The parabola has equation
y = ax(x-12)
Putting (6, 4), we get a = -1/9
Hence, equation of parabola:
Find the Area using:
Then, find the volume using
A is the cross sectional area and d is the depth of the prism.
The price will become trivial then.