Learning Outcome & Agenda | INSERT DATE HERE |
I will analyze the relationship between the volume formulas of cylinders and cones and then apply the formulas to solve real-world problems by [how I will show my learning].
Announcements
INSERT ANNOUNCEMENT HERE
What is Volume? | Notes |
Volume is the amount of space an object takes up or can hold.
What We Need to Review Part 1 | Notes |
Diameter = the length across a circle
= 2 times the radius
= 2r
Area of a Circle = πr2
Base Area (B) = πr2
π ≈ 3.14
Some answers are in terms of π (Example: 9π).
Some answers use 3.14159… for π and round.
What We Need to Review Part 2 | Notes |
Exponents: 52 = 5 * 2
= 10
53 = 5 * 3
= 15
Exponents: 52 = 5 * 5
= 25
53 = 5 * 5 * 5
= 25 * 5
= 125
Formula for the Volume of a Cylinder | Notes |
Volume of a Cylinder = Bh
= πr2h
Example for Finding the Volume of a Cylinder | Notes |
Volume = Bh
= πr2h
= π(3)2(5)
= π(9)(5)
= 45π
= 45(3.14)
≈ 141.3 ft3
Steps for Finding the Volume of a Cylinder | Notes |
Volume = Bh
= πr2h
= π(3)2(5)
= π(9)(5)
= 45π
= 45(3.14)
≈ 141.3 ft3
Step 1: Plug in radius & height
Step 2: Square the radius
Step 3: Multiply the numbers
Step 4: Multiply by 3.14 for π
Step 5: Put unit in cubic form
Comparing the Formula for the Volume of a Cylinder & Cone | Notes |
Volume = πr2h
3
Volume = πr2h
Formula for the Volume of a Cone | Notes |
Volume of a Cone = Bh
3
= πr2h
3
Example for Finding the Volume of a Cone | Notes |
Volume = Bh
3
= πr2h
3
= π(3)25
3
= π(9)5
3
= 45π
3
= 15π
= 15(3.14)
≈ 47.1 ft3
Steps for Finding the Volume of a Cone | Notes |
Volume = Bh
3
= πr2h
3
= π(3)2(5)
3
= π(9)(5)
3
= 45π
3
= 15π
= 15(3.14)
≈ 47.1 ft3
Step 1: Plug in radius & height
Step 2: Square the radius
Step 3: Multiply the numbers
Step 4: Divide by 3
Step 5: Multiply by 3.14 for π
Step 6: Put unit in cubic form
We Will Find the Volume of a Cone | Notes |
Volume = Bh
= πr2h
3
= π(5)2(8)
3
= π(25)(8)
3
= 200π
3
≈ 66.67π
≈ 66.67(3.14)
≈ 209.33 ft3
We Will Find the Volume of a Cone | Notes |
Volume = Bh
3
= πr2h
3
= π(5)2(8)
3
= π(25)(8)
3
= 200π
3
= 66.67π
= 66.67(3.14)
≈ 209.33 ft3
Step 1: Plug in radius & height
Step 2: Square the radius
Step 3: Multiply the numbers
Step 4: Divide by 3
Step 5: Multiply by 3.14 for π
Step 6: Put unit in cubic form
Your Team Will Find the Volume of a Cone | Notes |
Example 1 Example 2
Your Team Will Find the Volume of a Cone | Notes |
Example 1
Volume = Bh
3
= πr2h
3
= π(4)2(10)
3
= π(16)(10)
3
= 160π
3
= 53.33(3.14)
≈ 167.47 ft3
Your Team Will Find the Volume of a Cone | Notes |
Example 2
Volume = Bh
3
= πr2h
3
= π(6)2(12)
3
= π(36)(12)
3
= 432π
3
= 144(3.14)
≈ 452.16 ft3