# Lesson 12

How Much Will Fit?

### 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.

### Solution

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### 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?

A:

8 cm

B:

14 oz

C:

4.5 oz

D:

14 cm

### Solution

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### 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? ### Solution

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(From Unit 5, Lesson 7.)

### Problem 4

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

A:

$$(3,1)$$

B:

$$(1,1)$$

C:

$$(1,\text-3)$$

D:

$$(4,0)$$

E:

$$(6,7)$$

### Solution

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(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.

### Solution

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### Problem 6

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

### Solution

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(From Unit 4, Lesson 14.)