# Lesson 13

The Volume of a Cylinder

### Lesson Narrative

In this lesson students learn that the volume of a cylinder is the area of the base times the height, just like a prism. This is accomplished by considering 1-unit-tall layers of a rectangular prism side by side with 1-unit-tall layers of a cylinder. After thinking about how to compute the volume of specific cylinders, students learn the general formulas $$V=Bh$$ and $$V=\pi r^2 h$$.

In the warm-up, students recall that a circle’s area can be determined given its radius or diameter. Students also become familiar with what is meant by radius and height as those terms apply to cylinders. Finally, students compute the volume of a cylinder by multiplying the area of its base by its height. A volume expressed using the exact number $$\pi$$ versus the same volume computed using 3.14 as an approximation for $$\pi$$ is discussed. The following lesson provides opportunities to practice these skills and solve related problems.

### Learning Goals

Teacher Facing

• Calculate the volume of a cylinder, and compare and contrast (orally) the formula for volume of a cylinder with the formula for volume of a prism.
• Explain (orally) how to find the volume of a cylinder using the area of the base and height of the cylinder.

### Student Facing

Let’s explore cylinders and their volumes.

### Required Preparation

A good way to manage the various formulas in this unit is to create a display for each formula as each one is introduced. Frequently draw students’ attention to the displays and use them as a reference.

For the Circular Volumes activity, consider building a rectangular prism from 48 snap cubes to match the diagram in the print statement.

### Student Facing

• I can find the volume of a cylinder in mathematical and real-world situations.
• I know the formula for volume of a cylinder.

Building On

### Glossary Entries

• cone

A cone is a three-dimensional figure like a pyramid, but the base is a circle.

• cylinder

A cylinder is a three-dimensional figure like a prism, but with bases that are circles.

• sphere

A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.