Lesson 12

How Much Will Fit?

Let’s reason about the volume of different shapes.

Problem 1

  1. Sketch a cube and label its side length as 4 cm (this will be Cube A).
  2. Sketch a cube with sides that are twice as long as Cube A and label its side length (this will be Cube B).
  3. Find the volumes of Cube A and Cube B.

Problem 2

Two paper drink cups are shaped like cones. The small cone can hold 6 oz of water. The large cone is \(\frac43\) the height and \(\frac43\) the diameter of the small cone. Which of these could be the amount of water the large cone holds?


8 cm


14 oz


4.5 oz


14 cm

Problem 3

The graph represents the volume of a cylinder with a height equal to its radius.

  1. When the diameter is 2 cm, what is the radius of the cylinder?
  2. Express the volume of a cube of side length \(s\) as an equation.
  3. Make a table for volume of the cube at \(s = \) 0 cm, \(s = \) 1 cm, \(s = \) 2 cm, and \(s = \) 3 cm.
  4. Which volume is greater: the volume of the cube when \(s =\) 3 cm, or the volume of the cylinder when its diameter is 3 cm?
A coordinate plane, horizontal, diameter of a cylinder, 0 to 3 by ones, vertical, volume of the cylinder, 0 to 11 by ones. Curve begins at the origin, through (2 comma 3) and (3 comma 10 point 6).


(From Unit 5, Lesson 7.)

Problem 4

Select all the points that are on a line with slope 2 that also contains the point \((2, \text-1)\).











(From Unit 3, Lesson 10.)

Problem 5

Several glass aquariums of various sizes are for sale at a pet shop. They are all shaped like rectangular prisms. A 15-gallon tank is 24 inches long, 12 inches wide, and 12 inches tall. Match the dimensions of the other tanks with the volume of water they can each hold.

Problem 6

Solve: \(\begin{cases} y=\text-2x-20 \\ y=x+4 \\ \end{cases}\)

(From Unit 4, Lesson 14.)