The base of $ S $ is a circular disk with radius $ r $. Parallel cross-sections perpendicular to the base are isosceles triangles with height $ h $ and unequal side in the base.

(a) Set up an integral for the volume of $ S $.

(b) By interpreting the integral as an area, find the volume of $ S $.

a) $V=2 h \int_{0}^{r} \sqrt{r^{2}-x^{2}} d x$

b) $V=\frac{1}{2} \pi r^{2} h$

Applications of Integration

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