How you approach it depends on what you are solving. For A(h)=pi*h^2 (ie. a form of cone), you wouldn't need to perform a triple integral to find the volume. If you work it from basics it is a triple integral though, because the area came from integration over r and theta, then setting r=h.
So triple integrals are used to find volume from scratch, but are not always a necessary step if you recognise how the cross-sectional area behaves. That was the formula onemoretime had, which may or may not be useful depending on what needs to be solved.
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