Let's analyze each student's method for enlarging the volume of the rectangular prism and determine which changes the volume the most and by how much.
### Arya's Enlargement:
- Arya decided to enlarge the original prism by increasing just the height by a factor of 5.
- The original volume of the prism is [tex]\(150 \, \text{cm}^3\)[/tex].
- By enlarging only the height by a factor of 5, the new volume becomes:
[tex]\[ \text{New Volume (Arya)} = \text{Initial Volume} \times 5 = 150 \, \text{cm}^3 \times 5 = 750 \, \text{cm}^3 \][/tex]
### Jay's Enlargement:
- Jay decided to enlarge the original prism by increasing the length by a factor of 2 and the width by a factor of 2.
- The original volume of the prism is [tex]\(150 \, \text{cm}^3\)[/tex].
- By enlarging the length by 2 and the width by 2, the new volume becomes:
[tex]\[ \text{New Volume (Jay)} = \text{Initial Volume} \times (2 \times 2) = 150 \, \text{cm}^3 \times 4 = 600 \, \text{cm}^3 \][/tex]
### Comparing Enlargements:
- Arya's new volume: [tex]\(750 \, \text{cm}^3\)[/tex]
- Jay's new volume: [tex]\(600 \, \text{cm}^3\)[/tex]
### Determining the Larger Enlargement:
- Arya's enlargement results in a larger volume than Jay's.
- The difference in volume between Arya's and Jay's enlargement is:
[tex]\[ \text{Volume Difference} = 750 \, \text{cm}^3 - 600 \, \text{cm}^3 = 150 \, \text{cm}^3 \][/tex]
### Conclusion:
- Arya enlarged the volume by a factor of 5 while Jay enlarged the volume by a factor of 4.
- Arya's enlargement is [tex]\(150 \, \text{cm}^3\)[/tex] larger than Jay's enlargement.
Thus, the correct choice is:
- Arya enlarged the volume by a factor of 5 while Jay enlarged the volume by a factor of 4. Arya's enlargement is 150 cm³ larger than Jay's enlargement.
