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

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

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

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

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

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

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

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

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

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

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

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