Lesson 12: Practice Problems

Problem 1

Cylinder A, B, and C have the same radius but different heights. Put the cylinders in order of their volume from least to greatest.

Cylinders A, B, and C with the same radius but different heights.

  1. Cylinder A

  2. Cylinder B

  3. Cylinder C

Problem 2

Two cylinders, and , each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of and to Cylinders P and Q. Explain your reasoning.

A graph of volume in milliliters vs height in centimeters with two lines a and b. a starts lower than b but is more steep
Cylinders P and Q with height h and different sizes.

Problem 3

Which of the following graphs could represent the volume of water in a cylinder as a function of its height? Explain your reasoning.

  1. A graph with a straight line starting at (0,0) and going up
  2. B. A graph with a horizontal line
  3. C. A graph that starts at (0,0) and curves up

Problem 4 From Unit 6 Lesson 3

Together, the areas of the rectangles sum to 30 square centimeters.

A rectangle with side 3 and x. Another rectangle with side 2 and y.

  1. Write an equation showing the relationship between and .

  2. Fill in the table with the missing values.