### Day 75 - Volume: Disk Method/Washer Method - 05.06.15

Update(s)
• Unit 6 - Applications of Integration
• Area of a Region
• Volume of a Region: Disk Method
• Arc Length and Surface Area of a Region
• Unit 6 Test
• next Tuesday, May 12th
• Summative 3 Exam
• covers Units 5 and 6
• next Friday, May 15th
• Seniors Final Exam (optional)
• Monday, May 18th
• 8-12am
• Gym

Questions

Bell Ringer
1. Find the area between the two functions: from x = 0 to x = 5.

1. 5

2. 10

3. -5

4. 0

5. none of the above

2. Find the area between the two functions: from x = 0 to x = 2.

1. -4

2. 4

3. 0

4. 2

5. none of the above

3. Graph each equation. Find the area between the two curves:

1. 1/4

2. 1/2

3. 1/12

4. 5/6

5. none of the above

4. Graph each equation. Find the area between the two curves:

1. 1/4

2. 1/2

3. 1/12

4. 5/6

5. none of the above

5. Graph each equation. Find the area bounded by the region:

1. 4 - ln(2)

2. 4 - 4ln(2)

3. 4

4. 0

5. none of the above

Review
• Prerequisites
• Area of a Region
• How can the area of a region be calculated using definite integrals?
• Sketch areas of regions between given equations.
• Calculate area of regions between equations using calculus.
• Activity
• Checkpoints
• Extra Practice

Lesson
• Volume

• The Disk Method

• The Washer Method

Exit Ticket
• Posted on the board at the end of the block!

Lesson Objective(s)
• How can the volume of a solid of revolution be found?
Skills
1. Find volume using disk method.
2. Find volume using washer method.

#### In-Class Help Requests

Standard(s)
• APC.15​
• The student will use integration techniques and appropriate integrals to model physical, biological, and economic situations. The emphasis will be on using the integral of a rate of change to give accumulated change or on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. Specific applications will include
• a)​ the area of a region;
• b) ​the volume of a solid with known cross-section;
• c)​ the average value of a function; and
• d)​ the distance traveled by a particle along a line.