options: Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Translate between the geometric description and the equation for a conic section.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Apply geometric concepts in modeling situations.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

Experiment with transformations in the plane.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply theorems about circles.

Make geometric constructions.

Visualize relationships between two-dimensional and three-dimensional objects.

Solve real-world and mathematical problems involving area, surface area, and volume.

Classify two-dimensional figures into categories based on their properties.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Find arc lengths and areas of sectors of circles.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Warm-up
The purpose of this warm-up is to assess students’ understanding of the volume of a cylinder. Students learned that the volume of either a cylinder or prism is found by multiplying the area of the base by its height. In this warm-up, students are given information to find the area of a cylinder’s base, but they are not given the height. Students propose a volume for the cylinder and explain why it works. Since the diameter of the base is 8, the area of the base is
\(16\pi\)
.
If students have trouble getting started, ask them:
“Do you have enough information to calculate the area of the base?”
“What is the radius?”
Identify students who use these strategies:
find the area of the base first then set up the equation
\(V=16\pi h\)
.
choose a specific value for
\(h\)
then solve for the volume.
Launch
Arrange students in groups of 2. Tell students that in a previous lesson, they learned how to find the volume of a cylinder if they know the cylinder’s radius and height. Draw their attention to where volume formulas are displayed in the classroom as the unit progresses. Give students 1–2 minutes of quiet work time followed by time to explain their reasoning to their partner. Follow this with a whole-class discussion.
Student Facing
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
[IMG]
Student Response
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Activity Synthesis
The goal of this discussion is for students to communicate how the height of a cylinder is related to its volume. Invite students to share their solutions and their reasoning. Record and display the dimensions and volumes of cylinders that correspond to solutions given by students.


correct_option_index: 7