1. V OLUMES OF SOLIDS WITH KNOWN CROSS SECTIONS 4-H

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 SquareRectangleSemicircle TriangleEquilateral Triangle

5. 1)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

6. 2)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

7. 3)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 perpendicular to the x-axis

8. 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

9. 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.

10. H OME W ORK Volumes of solids with known cross sections worksheet