1. Warm Up Find the volume of the following 3 dimensional shapes.
Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Warm Up Find the volume of the following 3 dimensional shapes. 7
1.) 4 2 3 2 11
L=13
D=8
L=9
D=6
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Cross section
Plane cutting through object: a plane surface formed by cutting through an object at right angles to an axis, especially the longest axis.
A cross section is the shape you get when cutting straight across an object.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
1.) Draw a cross section perpendicular to the x-axis. Write an expression that represents the length of that cross section.
This is a “cross-section” of a 2D shape.
A “cross-section” goes across the section.
The width of each cross section (dx) is infinitely small
(the cross section is a line)
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
2.) Draw a cross section perpendicular to the y-axis. Write an expression that represents the length of that cross section.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure.
3.) Region R is the base of a solid. For each x, where 0 ≤ x≤ 9, the cross section of the solid taken perpendicular to the x-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure.
3.) Region R is the base of a solid. For each x, where 0 ≤ x≤ 9, the cross section of the solid taken perpendicular to the x-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure.
4.) Region R is the base of a solid. Cross sections of the solid, perpendicular to the x-axis, are semicircles. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure.
4.) Region R is the base of a solid. Cross sections of the solid, perpendicular to the x-axis, are semicircles. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure.
5.) Region R is the base of a solid. For each y, where 0 ≤ y ≤ 6, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose height is 3 times the length of its base in region R. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11. Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12. Practice: Cross Sectional Volume Worksheet
Chapter 6 Cross Sectional Volume
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
Practice: Cross Sectional Volume Worksheet
Wednesday, May 15, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals