To determine which sets of dimensions could be that of a right square prism with a volume of 360 cubic units, we need to verify that the volume of each given prism matches 360 cubic units. The volume [tex]\( V \)[/tex] of a right square prism is calculated as:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
Given the five options, let's verify each one:
1. Dimensions: 3 by 3 by 40
[tex]\[
V = 3 \times 3 \times 40 = 9 \times 40 = 360 \, \text{cubic units}
\][/tex]
These dimensions are valid since the volume is 360 cubic units.
2. Dimensions: 4 by 4 by 20
[tex]\[
V = 4 \times 4 \times 20 = 16 \times 20 = 320 \, \text{cubic units}
\][/tex]
These dimensions are not valid since the volume is 320 cubic units.
3. Dimensions: 5 by 5 by 14
[tex]\[
V = 5 \times 5 \times 14 = 25 \times 14 = 350 \, \text{cubic units}
\][/tex]
These dimensions are not valid since the volume is 350 cubic units.
4. Dimensions: 25 by 12 by 12
[tex]\[
V = 25 \times 12 \times 12 = 300 \times 12 = 3600 \, \text{cubic units}
\][/tex]
These dimensions are not valid since the volume is 3600 cubic units.
5. Dimensions: 3.6 by 10 by 10
[tex]\[
V = 3.6 \times 10 \times 10 = 36 \times 10 = 360 \, \text{cubic units}
\][/tex]
These dimensions are also valid since the volume is 360 cubic units.
Hence, the valid sets of dimensions that give a volume of 360 cubic units are:
1. 3 by 3 by 40
2. 3.6 by 10 by 10
