Pythagorean Theorem and Volume

Lesson 15

Math

Unit 7

8th Grade

Lesson 15 of 16

Objective


Solve real-world and mathematical problems involving the volume of spheres.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 7.G.B.4
  • 7.G.B.6

Criteria for Success


  • Understand the relationship between the volume of cylinders and the volume of spheres with the same diameter and height; determine the formula $${V={4\over{3}}\pi r^3}$$ for the volume of spheres.
  • Use the formula for the volume of spheres to find volume and radius. 

Tips for Teachers


Lesson Materials

  • Calculators (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

Watch this video demonstration: Cylinder, Cone, and Sphere Volume. (Note, the beginning of the video reviews the volume of a cone; the demonstration of a sphere's volume starts at 1:30.) 

a.   What is the relationship between the volume of a cylinder and the volume of a sphere with the same diameter and height?

b.   A sphere is enclosed in a cylinder. The diameter of the sphere is equal to the height of the cylinder.

  1. What is the height of the cylinder above, in terms of $$r$$?
  2. What is the formula for the volume of the cylinder above, in terms of $$r$$?
  3. What is the formula for the volume of the sphere inside the cylinder? 

Guiding Questions

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Student Response

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Problem 2

The cylinder below has a diameter of 14 inches and a height of 18 inches.

What is the volume of the largest sphere that will fit in the cylinder?

Guiding Questions

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Student Response

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Problem 3

The volume of an inflated beach ball is $${288\pi \space \mathrm{cm}^3}$$. What is the radius of the ball? 

 

 

 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


A standard soccer ball measures $${22 \space \mathrm{cm}}$$ in diameter. 

What is the volume of a standard soccer ball? Give your answer to the nearest whole cubic centimeter.

 

 

Student Response

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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.

  • Challenge: A cylindrical fishbowl has an 8 inch diameter on the base and an 8 inch height. There are currently 301.44 cubic inches of water in the fishbowl. You want to add in spherical marbles that each have a radius of $$\frac{1}{2}$$ inch. What is the maximum number of marbles you can add to the fishbowl before the water overflows?

Next

Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.

Lesson 16
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Lesson Map

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

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

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