Cross Sections By: Meghan Grubb

What are cross sections? A cross sectional area results from the intersection of a solid with a plane, usually an x-y plane. The volume can be found by breaking up the solid on a given interval into slices or cross sections.

Example First step – graph the given equations Second step – find the intersection points Third step – dx? or dy? Dx – cross sections perpendicular to x-axis Dy – cross sections perpendicular to y-axis Fourth Step – write integral sign and plug in bounds Fifth Step – remember area of a square Sixth Step – Find side length = top line minus bottom line Seventh Step – plug in dx

Example

First step – graph the given equations Second step – find the intersection points Third step – dx? or dy? Dx – cross sections perpendicular to x-axis Dy – cross sections perpendicular to y-axis Fourth Step – write integral sign and plug in bounds Fifth Step – remember area of a semi-circle Sixth Step – Find radius Seventh Step – plug in dy

Example Find intersection points