Volumes of solids with known cross sections 4-4

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

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

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

Cross Section Project

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

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

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

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

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.

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

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