# Volume of Cylinders, Cones, and Spheres

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## Objective

SWBAT give informal arguments for the volumes of cylinders, cones, and spheres.

#### Big Idea

Students will use manipulative, such as pennies and clay to investigate the volume of cylinders, cones and spheres.

## Do Now

5 minutes

In the Do Now, students complete a chart with the area and circumference of circles with a given radius. After about 3 minutes, we go over the chart. This Do Now is based on concepts from the previous lesson and will be used during the activity to find the volume of cones and spheres.

## Mini-Lesson

8 minutes

We begin the Mini-Lesson by comparing a cylinder to a prism. In a previous lesson, students found the volume of a prism by multiplying the area of the base by the height. Students don't instantly recognize that a cylinder is a prism with a circular base, but when they do realize, they are able to find the volume. Then we discuss how Cavalieri's Principle applies to cylinders and demonstrate this idea using a stack of pennies (G.GMD.1).

Next, we compare the volume of a cylinder to the volume of a cone with the same area of the base and height. Based on concepts from a previous lesson, students usually guess correctly that the volume of the cone is one third the volume of the cylinder. Students can use clay to model a cone and a cylinder to help them see the relationship (MP4).

To end the Mini-Lesson, I show the students the formula for finding the volume of a sphere. We discuss parts of the formula and how it relates to the area of a circle. In the activity, students will solve problems involving the volume of cylinders, cones and spheres using methods discuss in the Mini-Lesson.

25 minutes

## Summary

5 minutes

At the end of the lesson, I give a quick quiz. I check to see if students know which formula to use, how to correctly use the formula, and which units to use. Many of the student I teach still have difficulty after this lesson and often require an extra explanation of why we use specific units of measurement.