The purpose of this activity is for students to learn the relationship that the volume of a cone is of the volume of a cylinder and use it to calculate the volume of various cones. Students start by watching a video (or demonstration) that shows that it takes the contents of 3 cones to fill the cylinder when they have congruent bases and equal heights. Next, they practice using this information starting from either a known cylinder volume or a known cone volume before generalizing the relationship between any cone and cylinder pair with matching dimensions.

The purpose of this discussion is to make sure that students understand the relationship between the volume of a cone and the volume of a cylinder when their base area and heights are the same.

Invite previously selected students to share the volume equation they wrote for the last question. Display examples for all to see, and ask, “Are these equations the same? How can you know for sure?” (The calculated volume is the same when both equations are used.)

If no student suggests it, connect , where represents the volume of a cylinder with the same base and height as the cone, to the volume of the cone, . Reinforce that these are equivalent expressions.

Add the formula and a diagram of a cone to your classroom displays of the formulas being developed in this unit.

The purpose of this activity is for students to calculate the volume of cones given their height and radius. Students are given a cylinder with the same height and radius and use the volume relationship they learned earlier to calculate the volume of the cone. They then use the newly learned formula to calculate the volume of a cone given a height and radius. For the last problem, an image is not provided so that students have the opportunity to sketch one if they need it.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3). 

If students use 10 as the radius in the first problem, consider asking:

• “Can you explain how you figured out the volume for the cylinder and cone?”
• “Where do you see the height and radius in the picture of the cone?”

Focus this discussion on the final problem, which is the first time students are asked to calculate the volume of a cone in a context.

Begin by asking students to share any sketches they came up with to help them calculate the answer. Explain to students that sometimes we encounter problems that don’t have a visual example and only a written description. By using sketches and labeling relevant parts to help to visualize what is described in a problem, we can better understand what is being asked.