To find the volume of the box in terms of packages of colored pencils, we first need to calculate the volumes of both the box and a single package of colored pencils.
Step 1: Calculate the volume of the box.
The box is described as having:
- 4 layers
- Each layer is 2 units long and 7 units wide
The volume \( V \) of a rectangular prism is calculated as: \[ V = \text{length} \times \text{width} \times \text{height} \]
For the box:
- Length = 2 units
- Width = 7 units
- Height = 4 layers
Calculating the volume of the box: \[ V_{\text{box}} = 2 , \text{(length)} \times 7 , \text{(width)} \times 4 , \text{(height)} = 56 , \text{units}^3 \]
Step 2: Calculate the volume of a package of colored pencils.
The package of colored pencils is described as having:
- 2 layers
- Each layer is 1 unit long and 1 unit wide
Calculating the volume of a package: \[ V_{\text{package}} = 1 , \text{(length)} \times 1 , \text{(width)} \times 2 , \text{(height)} = 2 , \text{units}^3 \]
Step 3: Determine the number of packages of colored pencils that fit into the box.
To find how many packages fit into the box, we divide the volume of the box by the volume of one package: \[ \text{Number of packages} = \frac{V_{\text{box}}}{V_{\text{package}}} = \frac{56 , \text{units}^3}{2 , \text{units}^3} = 28 \]
So, the volume of the box in terms of packages of colored pencils is 28 packages.