Lesson 20The Volume of a Sphere
Learning Goal
Let’s explore spheres and their volumes.
Learning Targets
I can find the volume of a sphere when I know the radius.
Warm Up: Sketch a Sphere
Problem 1
Here is a method for quickly sketching a sphere:
Draw a circle.
Draw an oval in the middle whose edges touch the sphere.
Practice sketching some spheres. Sketch a few different sizes.
For each sketch, draw a radius and label it
.
Activity 1: A Sphere in a Cylinder
Problem 1
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
What is the height of the cylinder?
What is the volume of the cylinder?
What is the volume of the cone?
What is the volume of the sphere? Explain your reasoning.
Activity 2: Spheres in Cylinders
Problem 1
Here are a cone, a sphere, and a cylinder that all have the same radii and heights. Let the radius of the cylinder be
What is the height of the cylinder in terms of
? What is the volume of the cylinder in terms of
? What is the volume of the cone in terms of
? What is the volume of the sphere in terms of
? A volume of the cone is
the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?
Lesson Summary
Think about a sphere with radius
We know from an earlier lesson that the volume of a cone with the same base and height as a cylinder has
If we filled the cone and sphere with water, and then poured that water into the cylinder, the cylinder would be completely filled. That means the volume of the sphere and the volume of the cone add up to the volume of the cylinder. In other words, if