Unit 6, Lesson 15
The Volume of a Cone
Accelerated 7
Preparation
Lesson Narrative
In this lesson students start working with cones and learn that the volume of a cone is the volume of a cylinder with a congruent base and the same height. First, students learn a method for quickly sketching a cone and the meaning of the radius and height of a cone. Then they watch a video (or if possible, a live demonstration) showing that it takes three cones of water to fill a cylinder with the same radius and height. At this point, it is taken as a mysterious and beautiful fact that the volume of a cone is one third the volume of the associated cylinder. A proof of this fact requires mathematics beyond grade level.
Next, students write the volume of a cone given a specific volume of a cylinder with the same base and height, and vice versa. Then they use the formula for the volume of a cylinder learned in previous lessons to write the general formula for the volume, , of a cone in terms of its height, , and radius, .
In the last activity, students practice computing the volumes of some cones. They also practice critiquing a response about calculating volume to clarify its meaning, correct an error, and adding more detail (MP3).
- Calculate the volume of a cone and cylinder given the height and radius, and explain (orally) the solution method.
- Compare the volumes of a cone and a cylinder with the same base and height, and explain (orally and in writing) the relationship between the volumes.
Let’s explore cones and their volumes.
Required Preparation
If possible, provide students access to geometric solids with the same base and height measurements.
During the Launch, prepare to show a video. Alternatively, do a demonstration with a cone that could be filled with water and poured into a cylinder with matching base and height dimensions.