The problem I am trying to solve is: A hemispherical bowl of radius 8 inches is filled to depth of h inches, where h is between 0 and 8. Use the shell method to find the volume of water as a function of h.

I'm know that to use the shell method I need to use the formula: Integral from a to b 2 pi x (f(x) - g(x)) where 2 pi x corresponds to the circumference and f(x)-g(x) corresponds to the shell height.

I believe the radius would remain x and 2 pi x would stay the same. I'm very confused on how to find the limits of integration and the shell height. I thought the limits would be from h to 8 and the shell height would be y=sqrt 8-x, however using those values I was unable to find the correct answer.