To understand the relationship between the volumes of the two rectangular prisms, we first need to calculate the volume of each prism using the formula for the volume of a rectangular prism, which is given by:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
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Volume of the first rectangular prism:
- Base dimensions: 55 m (length) and 44 m (width)
- Height: 33 m
The volume \( V_1 \) is calculated as follows:
\[ V_1 = \text{Base Area} \times \text{Height} = (55 , \text{m} \times 44 , \text{m}) \times 33 , \text{m} \]
Calculating the base area:
\[ \text{Base Area} = 55 \times 44 = 2420 , \text{m}^2 \]
Therefore, the volume becomes:
\[ V_1 = 2420 , \text{m}^2 \times 33 , \text{m} = 79760 , \text{m}^3 \]
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Volume of the second rectangular prism:
- Base dimensions: 44 m (length) and 33 m (width)
- Height: 55 m
The volume \( V_2 \) is calculated as follows:
\[ V_2 = \text{Base Area} \times \text{Height} = (44 , \text{m} \times 33 , \text{m}) \times 55 , \text{m} \]
Calculating the base area:
\[ \text{Base Area} = 44 \times 33 = 1452 , \text{m}^2 \]
Therefore, the volume becomes:
\[ V_2 = 1452 , \text{m}^2 \times 55 , \text{m} = 79860 , \text{m}^3 \]
Now, let's compare the two volumes:
- Volume of the first prism \( V_1 = 79760 , \text{m}^3 \)
- Volume of the second prism \( V_2 = 79860 , \text{m}^3 \)
Relationship between the volumes:
- The two prisms have different dimensions, and their calculated volumes respectively are \( 79760 , \text{m}^3 \) and \( 79860 , \text{m}^3 \).
- Notice that both prisms are made from the same three dimensions (55 m, 44 m, 33 m), but arranged differently.
Conclusion:
The first rectangular prism has a volume of \( 79760 , \text{m}^3 \) and the second has a volume of \( 79860 , \text{m}^3 \). Therefore, the volumes are slightly different due to the arrangement of their respective height and base dimensions, illustrating how dimensional arrangement impacts the volume when the overall dimensions remain consistent.