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If we have to find the volume of a cylinder then we could imagine as if slices of same size have been mounted one over the other and knowing volume of one piece we could find the entire volume just by multiplying by an integer.

But in case of cone, as we put them into thin slices of thickness dx then volume of each would differ as the radii are different for different slices. Hence we need integral calculus with which we could easily get the right formula 1/3 pi r2 h with base radius r and height h

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Q: Why do you use integral calculus?
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