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Unit 5 - Lesson 20 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 5
Lesson 20: The Volume of a Sphere
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 5
Lesson 20: The Volume of a Sphere
CC BY 2021 Illustrative Mathematics®
Lesson: The Volume of a Sphere

Sketch a Sphere (Warm Up)

Here is a method for quickly sketching a sphere:

  • Draw a circle.
  • Draw an oval in the middle whose edges touch the sphere.
1.

  • Practice sketching some spheres. Sketch a few different sizes.
  • For each sketch, draw a radius and label it r.

A Sphere in a Cylinder

Here are a cone, a sphere, and a cylinder that all have the same radii and heights. The radius of the cylinder is 5 units. When necessary, express all answers in terms of π.
2.

What is the height of the cylinder?

3.

What is the volume of the cylinder?

4.

What is the volume of the cone?

5.

What is the volume of the sphere? Explain your reasoning.

Spheres in Cylinders

Here are a cone, a sphere, and a cylinder that all have the same radii and heights. Let the radius of the cylinder be r units. When necessary, express answers in terms of π.
6.

What is the height of the cylinder in terms of r?

7.

What is the volume of the cylinder in terms of r?

8.

What is the volume of the cone in terms of r?

9.

What is the volume of the sphere in terms of r?

10.

A volume of the cone is 1/3 the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?

Cool Down: Volumes of Spheres

Volumes of Spheres

Recall that the volume of a sphere is given by the formula
11.

Here is a sphere with radius 4 feet. What is the volume of the sphere? Express your answer in terms of π.

12.

A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this balloon holds. Use 3.14 as an approximation for π, and give a numerical answer.