To determine the volume of a crate packed to capacity with 81 cubes, each measuring 4 inches on each edge, follow these steps:
1. Determine the Volume of One Cube:
- The volume of a cube is calculated using the formula:
[tex]\[
\text{Volume} = \text{edge length}^3
\][/tex]
- Given that the edge length of each cube is 4 inches, we calculate:
[tex]\[
4 \text{ inches} \times 4 \text{ inches} \times 4 \text{ inches} = 64 \text{ cubic inches}
\][/tex]
- Thus, the volume of one cube is 64 cubic inches.
2. Calculate the Total Volume of All Cubes:
- Since there are 81 cubes, the total volume is:
[tex]\[
81 \text{ cubes} \times 64 \text{ cubic inches per cube} = 5,184 \text{ cubic inches}
\][/tex]
- Therefore, the volume of the crate that is packed to capacity with these 81 cubes is 5,184 cubic inches.
The provided answer choices were:
A. 64 in³
B. 81 in³
C. 1,296 in³
None of these match the correct solution. Please note there may have been a mistake in the answer options. The correct volume of the crate is [tex]\( \boxed{5184} \)[/tex] cubic inches.
