To determine which set of dimensions could form a right square prism with a volume of 360 cubic units, we must verify the volume calculation for each set of dimensions provided. The formula for the volume of a right square prism is given by:
[tex]\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \][/tex]
Since it's a right square prism, the length and width are equal, so we can use one dimension for both length and width. Let’s check each option:
1. Dimensions: 3 by 3 by 40
[tex]\[
\text{Volume} = 3 \times 3 \times 40 = 9 \times 40 = 360 \quad \text{(This matches)}
\][/tex]
2. Dimensions: 4 by 4 by 20
[tex]\[
\text{Volume} = 4 \times 4 \times 20 = 16 \times 20 = 320 \quad \text{(This does not match)}
\][/tex]
3. Dimensions: 5 by 5 by 14
[tex]\[
\text{Volume} = 5 \times 5 \times 14 = 25 \times 14 = 350 \quad \text{(This does not match)}
\][/tex]
4. Dimensions: 25 by 12 by 12
[tex]\[
\text{Volume} = 25 \times 12 \times 12 = 300 \times 12 = 3600 \quad \text{(This does not match)}
\][/tex]
5. Dimensions: 3.6 by 10 by 10
[tex]\[
\text{Volume} = 3.6 \times 10 \times 10 = 36 \times 10 = 360 \quad \text{(This matches)}
\][/tex]
From these calculations, the dimensions given that could form a right square prism with a volume of 360 cubic units are:
- 3 by 3 by 40
- 3.6 by 10 by 10
These are the two valid sets of dimensions based on the volume calculation. Therefore, only these two options satisfy the given condition.
