To determine the range of possible values for the volume of these boxes, follow these steps:
1. Identify Dimensions: The dimensions of each cardboard box are:
- Length \( L = 20 \) inches
- Width \( W = 15 \) inches
- Heights ranging from \( H_{\text{min}} = 4 \) inches to \( H_{\text{max}} = 6 \) inches
2. Calculate Minimum Volume:
- Minimum Height \( H_{\text{min}} = 4 \) inches
- Minimum Volume \( V_{\text{min}} = L \times W \times H_{\text{min}} = 20 \times 15 \times 4 \)
- So, \( V_{\text{min}} = 1200 \) cubic inches
3. Calculate Maximum Volume:
- Maximum Height \( H_{\text{max}} = 6 \) inches
- Maximum Volume \( V_{\text{max}} = L \times W \times H_{\text{max}} = 20 \times 15 \times 6 \)
- So, \( V_{\text{max}} = 1800 \) cubic inches
Now we can plot this range on a number line. We plot the numbers 1200 (minimum volume) and 1800 (maximum volume) to show the range.
Using the Line Segment Tool:
1. Place a point at 1200 to denote the lower bound of the volume.
2. Place another point at 1800 to denote the upper bound of the volume.
3. Draw a line segment connecting these two points to illustrate the continuous range of possible volumes from 1200 to 1800 cubic inches.
Your number line should look like this:
```
|------|---------------------------------------------------------------------------|------|
... 1200 1500 1800 ...
```
This number line indicates that the possible volumes of the cardboard boxes range continuously from 1200 to 1800 cubic inches.
