Unit 5
The Volume of a Cylinder
Functions and Volume
Lesson 13
8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Expressions and Equations
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Warm Up
Unit 5 ● Lesson 13
1 min individual - 1 min team share - 3 mins class share
Page 184
Here is a circle. Points A, B, C, & D are drawn, as well as segments AD and BC.
Area of a circle:
A = 𝞹r²
2) 7 units. The square of the radius is 49 since the area is π times the square of the radius, and the area is 49π square units. The radius is 7 units, because 49 = 7²
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 13
We will be able to know the formula for volume of a cylinder so that we can find the volume of a cylinder.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 5 ● Lesson 13
Agenda Review
You are successful today when...,
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
A cylinder is a three-dimensional figure like a prism, but with bases that are circles.
A cylinder is made up of a rolled surface with a circular top and a circular base.
V = 𝞹r²h
OR… V = r²h𝞹
Base times height
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
B = 𝞹r²
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.2 Activity: Circular Volumes
You know the formula for volume of a cylinder.
10 mins total
3 mins individual - 3 minutes group - 4 mins class share
pg 185
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.4 Activity: A Cylinder's Volume
You know the formula for volume of a cylinder.
10 mins total
3 mins individual - 3 minutes group - 3 mins class share
pg 188
25𝞹. (𝞹5²)
100𝞹. (25𝞹 ⦁ 4)
2. Approximately 509 cubic feet. (509 ft.³)
The diameter of the silo’s base is 6 feet, which means the base has a radius of 3 feet.
The area of the base of the silo is 9𝞹 square feet.
162𝞹 (18 ⦁ 3²𝞹), using 𝞹 ≈ 3.14, the volume of the silo is approximately 509 cubic feet.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
The Volume of a Cylinder
You know the formula for volume of a cylinder.
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Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Liquid Volume
You know the formula for volume of a cylinder.
16𝞹 cm²
112𝞹 cm³
≈351.68 cm³
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Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 13
Learning
Targets
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
A cone is a three-dimensional figure like a pyramid, but the base is a circle.
A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.
A cylinder is a three-dimensional figure like a prism, but with bases that are circles.
A cylinder is made up of a rolled surface with a circular top and a circular base.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Glossary
A function is a rule with exactly one output for each allowable input
Domain
Range
y depends on x
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.
All curriculum excerpts are under the following licenses:
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
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