I'm going to agree with the first one, but include a small chastisement. Please exploit symmetry where you can. Multiply the whole thing by 2 and change the first lower limit to zero (0).

On the second, I have to object. Why do you think the extremes would be at z = 0? Frankly, z = 16 seems more likely. Further, why would you not change this one to Polar Coordinates?