1. Volumes of solids with known cross sections
4-4

2. Cross sections perpendicular to the x-axis
Where A is a function of x and gives the area of a representative cross section
Usually squares, semicircles, trapezoids, triangles, or rectangles

3. Cross sections perpendicular to the y-axis
Where A is a function of y and gives the area of a representative cross section

4. Area formulas for common cross sections
Square Rectangle Semicircle
Triangle Equilateral Triangle

5. Cross Section Project

6. Find the volume of the solid whose base is a triangle bounded by 𝑦=−2𝑥+2, x= 0, and
y = 0, and whose cross sections are squares which are perpendicular to the x-axis
base

7. Set up (but do not integrate) the integral for volume of the solid with the same base but whose cross sections are semi-circles perpendicular to the x-axis

8. Set up (but do not integrate) the integral for volume of the solid whose base is bounded by
and whose cross sections are rectangles of height ¼ the base, perpendicular to the x-axis

9. 4) Set up (but do not integrate) the integral for volume of the solid whose base is a circle and whose cross sections are squares perpendicular to the y-axis

10. 5) Set up (but do not integrate) the integral for volume of the solid with the same base but whose cross sections are equilateral triangles perpendicular to the y-axis.

11. 6) Find the integral for the volume of the solid bounded by
6) Find the integral for the volume of the solid bounded by , 𝑦=0, 𝑎𝑛𝑑 𝑥=1 whose cross sections are semicircles perpendicular to the y-axis. Then evaluate using a calculator

12. Home Work Volumes of solids with known cross sections worksheet 4-4
Use a section header for each of the topics, so there is a clear transition to the audience.
Volumes of solids with known cross sections worksheet 4-4