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# Volume of Cylinders, Cones, and Spheres

Lesson 4 of 5

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

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#### Mini-Lesson

*8 min*

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.

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#### Summary

*5 min*

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.

#### Resources

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment