options: Explain volume formulas and use them to solve problems.

Find arc lengths and areas of sectors of circles.

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.

Understand and apply the Pythagorean Theorem.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

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

Reason with shapes and their attributes.

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

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

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

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Apply trigonometry to general triangles.

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Apply geometric concepts in modeling situations.

Make geometric constructions.

Understand congruence in terms of rigid motions.

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

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

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.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
problem_activity: Task
Janine is planning on creating a water-based centerpiece for each of the 30 tables at her wedding reception. She has already purchased a cylindrical vase for each table. The radius of the vases is 6 cm and the height is 28 cm. She intends to fill them half way with water and then add a variety of colored marbles until the waterline is approximately three-quarters of the way up the cylinder. She can buy bags of 100 marbles in 2 different sizes, with radii of 9 mm or 12 mm. A bag of 9 mm marbles costs \$3 and a bag of 12 mm marbles costs \$4.
If Janine only bought 9 mm marbles how much would she spend on marbles for the whole reception? What if Janine only bought 12 mm marbles? (Note: $1\text{ cm}^3 = 1\text{ ml}$)
Janine's parents, who are paying for the wedding, have told her she can spend at most $d$ dollars on marbles.  Write a system of equalities and/or inequalities that she can use to determine how many marbles of each type she can buy.
Based on your answer to part (b), how many bags of each size marble should Janine buy if she has \$180 and wants to mix in as many small marbles as possible.


correct_option_index: 0