The purpose of this lesson is for students to recognize that the volume of a sphere with radius is and begin to use the formula. Students inspect an image of a sphere that snugly fits inside a cylinder (they each have the same radius, and the height of the cylinder is equal to the diameter of the sphere), and use their intuition to guess how the volume of the sphere relates to the volume of the cylinder, building on the work in the previous lesson.

Then they watch a video that shows a sphere inside a cylinder, and the contents of a cone (with the same base and height as the cylinder) are poured into the remaining space, helping students make sense of the relationships between the volumes (MP1). This demonstration shows that for these figures, the cylinder contains the volumes of the sphere and cone together. From this observation, the volume of a specific sphere is computed.

Then the formula for the volume of a sphere is derived. (At this point, this is taken to be true for any sphere even though we only saw a demonstration involving a particular sphere, cone, and cylinder. A general proof of the formula for the volume of a sphere would require mathematics beyond grade level.)

In the last activity, students reason about the relationship between the volumes for any cone, sphere, or cylinder group with matching dimensions by rewriting and using the structure of the volume formulas for a cone and cylinder to determine the formula for a sphere (MP7).