Answer :
To determine which prism has a volume of 5 cubic units, let's calculate the volume of each prism step-by-step.
### Prism 1
The dimensions of Prism 1 are [tex]\(1 \frac{1}{2}\)[/tex] units by 2 units by 3 units.
First, we convert [tex]\(1 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2} \][/tex]
Now, we calculate the volume:
[tex]\[ \text{Volume of Prism 1} = \left(\frac{3}{2}\right) \times 2 \times 3 = \frac{3 \times 2 \times 3}{2} = \frac{18}{2} = 9 \text{ cubic units} \][/tex]
### Prism 2
The dimensions of Prism 2 are 1 unit by 2 units by [tex]\(1 \frac{1}{4}\)[/tex] units.
Convert [tex]\(1 \frac{1}{4}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{5}{4} \][/tex]
Now, we calculate the volume:
[tex]\[ \text{Volume of Prism 2} = 1 \times 2 \times \left(\frac{5}{4}\right) = \frac{2 \times 5}{4} = \frac{10}{4} = 2.5 \text{ cubic units} \][/tex]
### Prism 3
The dimensions of Prism 3 are 4 units by 1 unit by 2 units.
Calculate the volume:
[tex]\[ \text{Volume of Prism 3} = 4 \times 1 \times 2 = 8 \text{ cubic units} \][/tex]
### Prism 4
The dimensions of Prism 4 are 2 units by 1 unit by 2 units.
Calculate the volume:
[tex]\[ \text{Volume of Prism 4} = 2 \times 1 \times 2 = 4 \text{ cubic units} \][/tex]
### Conclusion
After calculating the volumes, we find:
- Prism 1: 9 cubic units
- Prism 2: 2.5 cubic units
- Prism 3: 8 cubic units
- Prism 4: 4 cubic units
None of the prisms have a volume of 5 cubic units. Therefore, the answer is that no prism has a volume of 5 cubic units.
### Prism 1
The dimensions of Prism 1 are [tex]\(1 \frac{1}{2}\)[/tex] units by 2 units by 3 units.
First, we convert [tex]\(1 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2} \][/tex]
Now, we calculate the volume:
[tex]\[ \text{Volume of Prism 1} = \left(\frac{3}{2}\right) \times 2 \times 3 = \frac{3 \times 2 \times 3}{2} = \frac{18}{2} = 9 \text{ cubic units} \][/tex]
### Prism 2
The dimensions of Prism 2 are 1 unit by 2 units by [tex]\(1 \frac{1}{4}\)[/tex] units.
Convert [tex]\(1 \frac{1}{4}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{5}{4} \][/tex]
Now, we calculate the volume:
[tex]\[ \text{Volume of Prism 2} = 1 \times 2 \times \left(\frac{5}{4}\right) = \frac{2 \times 5}{4} = \frac{10}{4} = 2.5 \text{ cubic units} \][/tex]
### Prism 3
The dimensions of Prism 3 are 4 units by 1 unit by 2 units.
Calculate the volume:
[tex]\[ \text{Volume of Prism 3} = 4 \times 1 \times 2 = 8 \text{ cubic units} \][/tex]
### Prism 4
The dimensions of Prism 4 are 2 units by 1 unit by 2 units.
Calculate the volume:
[tex]\[ \text{Volume of Prism 4} = 2 \times 1 \times 2 = 4 \text{ cubic units} \][/tex]
### Conclusion
After calculating the volumes, we find:
- Prism 1: 9 cubic units
- Prism 2: 2.5 cubic units
- Prism 3: 8 cubic units
- Prism 4: 4 cubic units
None of the prisms have a volume of 5 cubic units. Therefore, the answer is that no prism has a volume of 5 cubic units.
