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

Make geometric constructions.

Find arc lengths and areas of sectors of circles.

Explain volume formulas and use them to solve problems.

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

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

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

Apply trigonometry to general triangles.

Understand and apply theorems about circles.

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.

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Prove geometric theorems.

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

Reason with shapes and their attributes.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

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

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

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

Understand congruence in terms of rigid motions.

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

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

Analyze, compare, create, and compose shapes.
problem_activity: Warm-up
This warm-up helps students recall the use of the Pythagorean Theorem and right triangle trigonometry. They’ll use these concepts in subsequent activities.
Launch
Provide students with access to scientific calculators.
Student Facing
Calculate the height of each solid. Round your answers to the nearest tenth if needed.
A
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B
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Student Response
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Anticipated Misconceptions
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 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.
Activity Synthesis
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 the cylinder problem. Remind students that they can use their reference chart to recall the trigonometric ratio definitions.


correct_option_index: 23