To determine the possible dimensions of a right square prism with a volume of 360 cubic units, we need to verify each set of given dimensions to see if their volume equals 360 cubic units. The volume [tex]\( V \)[/tex] of a right square prism can be calculated using the formula:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
We will check if any of the given dimensions meet this criterion.
1. Dimensions: 3 units by 3 units by 40 units
[tex]\[
V = 3 \times 3 \times 40 = 9 \times 40 = 360 \text{ cubic units}
\][/tex]
These dimensions are valid.
2. Dimensions: 4 units by 4 units by 20 units
[tex]\[
V = 4 \times 4 \times 20 = 16 \times 20 = 320 \text{ cubic units}
\][/tex]
These dimensions do not match the required volume.
3. Dimensions: 5 units by 5 units by 14 units
[tex]\[
V = 5 \times 5 \times 14 = 25 \times 14 = 350 \text{ cubic units}
\][/tex]
These dimensions do not match the required volume.
4. Dimensions: 2.5 units by 12 units by 12 units
[tex]\[
V = 2.5 \times 12 \times 12 = 2.5 \times 144 = 360 \text{ cubic units}
\][/tex]
These dimensions are valid.
5. Dimensions: 3.6 units by 10 units by 10 units
[tex]\[
V = 3.6 \times 10 \times 10 = 3.6 \times 100 = 360 \text{ cubic units}
\][/tex]
These dimensions are valid.
Therefore, the three sets of dimensions that form a right square prism with a volume of 360 cubic units are:
- 3 by 3 by 40
- 2.5 by 12 by 12
- 3.6 by 10 by 10
