# Lesson 15

Putting All the Solids Together

### Lesson Narrative

In this lesson, students apply their knowledge of pyramid, cone, prism, and cylinder volume formulas. Trigonometry and the Pythagorean Theorem are incorporated as additional tools. Students practice thinking through the methods they will use to solve a problem before starting their calculations. Finally, they calculate the volume of a solid of rotation composed of a cylinder and a cone.

Students make sense of the geometry of solids as they find missing measurements and use them to calculate volumes (MP1).

### Learning Goals

Teacher Facing

• Calculate volumes of prisms, cylinders, cones, and pyramids.

### Student Facing

• Let’s calculate volumes of prisms, cylinders, cones, and pyramids.

### Student Facing

• I can use the Pythagorean Theorem and trigonometry to help calculate volumes of prisms, cylinders, cones, and pyramids, including solids of rotation.

### Glossary Entries

• apex

The single point on a cone or pyramid that is the furthest from the base. For a pyramid, the apex is where all the triangular faces meet.