# Lesson 11

Prisms Practice

### Lesson Narrative

This lesson gives students the opportunity to practice and apply what they have learned about volumes of prisms. They use trigonometry and the Pythagorean Theorem to find missing measurements, and they use decomposition to find volumes of more complex solids.

When students recognize they can add a line to a diagram to create a right triangle, enabling them to calculate values for missing dimensions, they are looking for and making use of structure (MP7).

### Learning Goals

Teacher Facing

• Calculate volumes of solids composed of right and oblique prisms and cylinders.

### Student Facing

• Let’s calculate volumes of prisms and cylinders.

### Student Facing

• I can calculate volumes of right and oblique prisms and cylinders and figures composed of prisms and cylinders.

Building On

Building Towards

### Glossary Entries

• Cavalieri’s Principle

If two solids are cut into cross sections by parallel planes, and the corresponding cross sections on each plane always have equal areas, then the two solids have the same volume.

• oblique (solid)

Prisms and cylinders are said to be oblique if when one base is translated to coincide with the other, the directed line segment that defines the translation is not perpendicular to the bases.

A cone is said to be oblique if a line drawn from its apex at a right angle to the plane of its base does not intersect the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.

• right (solid)

Prisms or cylinders are said to be right if when one base is translated to coincide with the other, the directed line segment that defines the translation is perpendicular to the bases.

A cone is said to be right if a line drawn from its apex at a right angle to the plane of its base passes through the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.