This Warm-up helps students recall the use of the Pythagorean Theorem and right-triangle trigonometry. They’ll use these concepts in subsequent activities.

The height is not drawn in on the cylinder, so students may not be able to visualize the right triangle involved in the problem. Encourage them to draw in the height and to think back to other problems from prior units involving angles and degree measurements.

Students may be uncertain how to round the first answer. Remind them that 16.0 is considered a “rounded” answer because the additional decimal digits to the right have been dropped.

The purpose of this discussion is to remind students of strategies they have for working with right triangles. Ask students what strategies they used, and how they chose those strategies. Invite them to explain why they can use the Pythagorean Theorem for the cone problem but not for the cylinder problem. Remind students that they can use their reference chart to recall the trigonometric ratio definitions.

The purpose of this activity is to give students the opportunity to reflect on their own understanding and apply that understanding to solve problems involving volumes, the Pythagorean Theorem, and trigonometry. Students rely on their knowledge of the solids and how the volume of each is calculated to determine which have all the information needed given and which require additional steps, such as adding auxiliary lines (MP7).

Look for students who choose a right prism with which they can straightforwardly compute , students who choose the oblique cylinder that doesn’t involve trigonometry, and students who choose a prism that involves trigonometry.

The purpose of this activity is for students to apply what they have learned about prisms and cross-sections to a context.