Volume of Cylinders, Cones, and Spheres
Lesson 4 of 5
Objective: SWBAT give informal arguments for the volumes of cylinders, cones, and spheres.
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.
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.
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.