# Lesson 25

Cylinders, Cones, and Spheres

### Lesson Narrative

In this lesson, students use the formula for the volume of a sphere to solve various problems. They have opportunities to analyze common errors that people make when using this formula. They also use the structure of an equation to find the radius of a sphere when they know its volume. Finally, they have opportunities to practice using all of the new volume formulas they have learned in this unit to solve mixed problems with spheres, cylinders, and cones, reasoning about the effect of different dimensions on the volume of different figures.

### Learning Goals

Teacher Facing

• Calculate the value of the radius of a sphere with a given volume using the structure of the equation, and explain (orally) the solution method.
• Determine what information is needed to solve a problem involving volumes of cones, cylinders, and spheres. Ask questions to elicit that information.

### Student Facing

Let’s find the volume of shapes.

### Required Preparation

Print and cut up slips from the Info Gap: Unknown Dimensions blackline master.  Prepare 1 set of slips for every 2 students. Provide students with access to make a visual display during the Lesson Synthesis.

### Student Facing

• I can find the radius of a sphere if I know its volume.
• I can solve mathematical and real-world problems about the volume of cylinders, cones, and spheres.