Lesson objective: Fluently calculate both the exact and approximate volumes of spheres.

This lesson helps to build fluency with calculating the volume of a sphere by illustrating its relationship to the volume of a cylinder. A sphere inscribed within a cylinder is used here because it highlights the relationship between the diameter of the sphere and the height of the cylinder. This work develops students' understanding that the volume of a sphere is \(\frac23\) of the volume of a cylinder.

Students engage in Mathematical Practice 1** **(make sense of problems and persevere in solving them) as they identify and use the dimensions of spheres to find their volumes.

**Key vocabulary:**

- area
- base
- cylinder
- diameter
- hemisphere
- radius
- sphere
- volume