Unit 5
Estimating a Hemisphere
Functions and Volume
Lesson 19
8.G.C: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
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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Two Shapes
Unit 5 ● Lesson 19
1 min individual - 1 min team share - 3 mins class share
Page 223
r = h so we can cube the radius
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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 19
We will be able to calculate the volume of a shape we know is larger and the volume of a shape we know is smaller so that we can estimate the volume of a hemisphere.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 5 ● Lesson 19
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.
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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.
19.2 Activity: Hemispheres in Boxes
I can Estimate the volume of a hemisphere using the formulas for volume.
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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 hemisphere is one-half of a sphere. The top of the silo is a hemisphere with a radius of 12 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.
19.2 Activity: Hemispheres in Boxes
I can Estimate the volume of a hemisphere using the formulas for volume.
7 mins total
Q1: 4 minutes group - 3 mins class share
pg 223
6cm x 6cm x 3cm
108cm³. 108 is 6² ⦁ 3.
Less than 108 cubic centimeters.
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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.
19.2 Activity: Hemispheres in Boxes
I can Estimate the volume of a hemisphere using the formulas for volume.
52% of 108cm³. (56.6 cm³) The hemisphere must have a volume that is less than the prism.
Diameter and radius
Diameter
Less than the volume of the box
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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.
19.3 Activity: Estimating Hemispheres
I can Estimate the volume of a hemisphere using the formulas for volume.
The height of the cylinder is equal to the radius of the hemisphere.
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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.
19.3 Activity: Estimating Hemispheres
I can Estimate the volume of a hemisphere using the formulas for volume.
15 mins total
5 minutes group - 3 mins class share
pg 224
Cylinder
V = 𝞹5³
V = 125𝞹
V ≈ 392.7 cm³
Cone
V = ⅓ ⦁ 𝞹5³
V = ⅓ ⦁ 125𝞹
V ≈ 41.7𝞹
V ≈ 130.9 cm³
Less than 392.7 cm³
Greater than
130.9 cm³
The volume of the hemisphere will be greater than the volume of the cone but less than the volume of the cylinder.
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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.
19.3 Activity: Estimating Hemispheres
I can Estimate the volume of a hemisphere using the formulas for volume.
The volume of the hemisphere has to be between the two volumes.
The volume of the hemisphere has to be between the two volumes, so… a possible hemisphere volume might be the average of these two.
⅓ + 3/3 = 4/3, divided by 2 = ⅔𝞹r³
(4/3 * ½ = 4/6 = ⅔ )
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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.
Estimating a Hemisphere
I can Estimate the volume of a hemisphere using the formulas for volume.
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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.
A Mirror Box
I can Estimate the volume of a hemisphere using the formulas for volume.
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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 19
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.
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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.
V = ⅓𝞹r²h
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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
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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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