1. What makes a rotation solid? What makes a rotation hollow?
Chapter 6.2 Solids of Revolution
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.
Can you guess what everyday object will be created by the pictured rotation?
Warm Up
What makes a rotation solid? What makes a rotation hollow?
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3. Chapter 6.2 Solids of Revolution
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.
The Disk Method
Integration stacks a massive amount of infinitely thin disks
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5. Do not round with a pie. Chapter 6.2 Solids of Revolution
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.
Do not round with a pie.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. Chapter 6.2 Solids of Revolution
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.
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis (y=0).
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. Washer Method SQUARE BEFORE YOU SUBTRACT!!! lol
Chapter 6.2 Solids of Revolution
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.
Washer Method
SQUARE BEFORE YOU SUBTRACT!!! lol
SUBTRACT VOLUME, NOT AREA!! lol
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. Chapter 6.2 Solids of Revolution
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.
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10. Chapter 6.2 Solids of Revolution
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.
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11. Disk Method Washer Method
Chapter 6.2 Solids of Revolution
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.
Disk Method
Washer Method
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

13. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

14. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

15. Chapter 6.2 Solids of Revolution
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.
Monday, February 25, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals