# Lesson 18

The Volume and Dimensions 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. Next, students compute the volume of a cylinder by multiplying the area of its base by its height. Finally, students compute volumes given radius and height, and find radius or height given a cylinder’s volume and the other dimension by reasoning about the structure of the volume formula.

### Learning Goals

Teacher Facing

• Calculate the value of one dimension of a cylinder, and explain (orally and in writing) the reasoning.
• 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.

### Student Facing

Let’s explore cylinder volumes and dimensions.

### Student Facing

• I can find missing information about a cylinder if I know its volume and some other information.
• I know the formula for volume of a cylinder.

Building On