1. 5/19/2015 Perkins AP Calculus AB Day 7 Section 7.2

2. Theorem: The volume of a solid with cross-section of area A(x) that is perpendicular to the x-axis is given by Finding the volume of a solid with known cross-section is a 3-step process: Step #1:Find the length (S) of the rectangle used to create the base of the figure. Step #2:Find the area A(x) of each cross-section (in terms of this rectangle). Step #3:Integrate the area function from the lower to the upper bound. ***This circle is the base of a 3-D figure coming out of the screen. ***This rectangle is a side of a geometric figure (a cross-section of the whole). a b Volume of a solid with cross-sections of area A(y) and perpendicular to the y-axis: c d S S

3. Find the volume of the solid whose base is bounded by the circle with cross-sections perpendicular to the x-axis. These cross-sections are a. squares Step #1:Find S. Step #2:Find A(x). Step #3:Integrate the area function. S -22 S

4. Find the volume of the solid whose base is bounded by the circle with cross-sections perpendicular to the x-axis. These cross-sections are Step #1:Find S. Step #2:Find A(x). Step #3:Integrate. b. equilateral triangles S -22 S

5. Perkins AP Calculus AB Day 7 Section 7.2

6. Theorem: The volume of a solid with cross-section of area A(x) that is perpendicular to the x-axis is given by Finding the volume of a solid with known cross-section is a 3-step process: a b

7. Find the volume of the solid whose base is bounded by the circle with cross-sections perpendicular to the x-axis. These cross-sections are a. squares Step #1:Find S. Step #2:Find A(x). Step #3:Integrate the area function.

8. Find the volume of the solid whose base is bounded by the circle with cross-sections perpendicular to the x-axis. These cross-sections are Step #1:Find S. Step #2:Find A(x). Step #3:Integrate. b. equilateral triangles