As long as all your bounds are correct for the figure, your answer is off. I obtained 400*pi/3 for that integral as is.
Question: Find the spherical coordinate limits for the integral that calculates the volume of the solid between the sphere and the hemisphere . Then evaluate the integral.
I found the integral with the correct limits for the solid in spherical coordinates as the following:
I would like to check my volume, the answer which i got is .