Curriculum  /  Math  /  10th Grade  /  Unit 6: Three-Dimensional Measurement and Application  /  Lesson 12

Three-Dimensional Measurement and Application

Lesson 12

Math

Unit 6

10th Grade

Lesson 12 of 18

Objective

Calculate the volume of a sphere and use this in the solution of problems.

Common Core Standards

Core Standards

  • G.GMD.A.1 — Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
  • G.GMD.A.2 — Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
  • G.GMD.A.3 — Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  • N.Q.A.3 — Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Foundational Standards

  • 8.G.C.9

Criteria for Success

  1. Use the volume of a sphere $${4\over3}\pi r^3$$.
  2. Describe that the volume of a cylinder with height of $$2r$$ and radius of $$r$$ is the same as the volume of a sphere with radius $$r$$ and a cone with radius $$r$$ and height of $$2r$$.
  3. Given either the radius, height, or another dimension, find other measurements in the problem.
  4. Apply constraints on dimensions provided in the context of the problem to modify general formulas to model the specific problem. 
  5. Identify when an estimate of volume is necessary and apply this to the problem.  

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Anchor Problems

25-30 minutes

Problem 1

What is the relationship between the following three volumes?

Guiding Questions

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Problem 2

Below is a soap bubble on a table with a diameter of 8 centimeters. What is the volume of the air inside the bubble? Assume the soap bubble itself has no thickness.

Guiding Questions

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References

Wikimedia Commons Photo: Bubble on a Liquid Surface by Stevearscott

Bubble on a Liquid Surface by Stevearscott is made available on Wikimedia Commons under the CC BY-SA 4.0 license. Accessed Sept. 18, 2018, 12:02 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

How many paper balls will fit in the can?

Guiding Questions

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References

101Questions Trashketball (Cylinder)

Trashketball (Cylinder) by Andrew Stadel is made available on 101Questions under the CC BY 3.0 license. Accessed June 2, 2017, 9:17 a.m..

Target Task

5-10 minutes

Snow globes consist of a glass sphere that is filled with liquid and other contents. If the inside radius of the snow globe is 3 inches, find the approximate volume of material in cubic inches that can fit inside.

References

EngageNY Mathematics Geometry > Module 3 > Topic B > Lesson 12 — Exit Ticket, Question #1

Geometry > Module 3 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students are given the volume of a sphere and must find the radius.

Next

Calculate the volume of compound objects and those with subtracted solids. Determine how the volume will be affected by scaling one or more dimensions.

Lesson 13
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area and Circumference of Circles

Topic B: Three-Dimensional Concepts and General Volume

Topic C: Cavalieri's Principle, Spheres, and Composite Volume

Topic D: Surface Area, Scaling, and Modeling with Geometry

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