Lesson objective: Fluently find the approximate and exact volumes of cylinders and their component parts.

This lesson helps to build procedural skill with finding the volume of cylinders. Three-dimensional modeling is used here because it supports the abstract nature of using formulas to find volumes and their component parts. This work develops students' understanding that volume is a measure of capacity, and incorporates all dimensions of a three-dimensional figure. This work also develops students' understanding that there is a connection between the formulas for right prisms and cylinders, namely that both include the area of the base and the height.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they dissect the visual representation of each cylinder to determine which components are given, as they determine how each component is to be incorporated into the formula for finding volume, as they decide how to appropriately apply mathematical reasoning to arrive at an answer, and as they describe what the answer actually means.

**Key vocabulary:**

- area
- base
- diameter
- height
- radius
- volume