Figure 6
The volumeof soliddoesnot necessarilyhaveto be circular. It can take any arbitraryshape.One useful
way to find the volumeis by a techniquecalled“slicing.”To explainthe idea,supposea solid is positioned
on the -axisand extendsfrom points to (Figure6). Let be the cross-sectionalarea
of the solidat somearbitrarypoint Just like we did in calculatingthe definiteintegralin the previous
chapter, dividethe interval into sub-intervalsand with widths
Eventually, we get planesthat cut the solid into n slices
Take one slice, We can approximateslice to be a rectangularsolid with thickness and cross-
sectionalarea Thusthe volume of the slice is approximately
Thereforethe volume of the entiresolid is approximately