Sure, let's solve these questions step by step given Spencer's scenario:
1. Length of the Box:
Spencer measures one edge of the cube-shaped box and finds that it is 4 inches long. In a cube, all edges are of equal length. Therefore, the length of the box is:
- Length = 4 inches
2. Width of the Box:
Similarly, since it is a cube, the width is the same as the length. Therefore, the width of the box is:
- Width = 4 inches
3. Height of the Box:
Again, because it is a cube, the height is the same as the length and width. Therefore, the height of the box is:
- Height = 4 inches
4. Volume of the Box:
The volume of a cube is calculated using the formula:
[tex]\[
\text{Volume} = \text{edge length}^3
\][/tex]
So, we can find the volume by cubing the edge length (4 inches):
- Volume = 4 inches × 4 inches × 4 inches
- Volume = 64 cubic inches
5. 4 Cubed:
Based on the calculation above, [tex]\(4^3\)[/tex] or 4 cubed is:
- 4 cubed = 4 × 4 × 4 = 64
Therefore:
- Length of the box = 4 inches
- Width of the box = 4 inches
- Height of the box = 4 inches
- Volume of the box = 64 cubic inches
- 4 cubed = 64
