To determine the correct statement regarding the two figures, we first need to calculate the volumes of both Figure A and Figure B based on their dimensions.
Figure A:
- Dimensions: 27.5 ft, 27.5 ft, and 55 ft
- Volume \( V_A \) can be calculated using the formula for the volume of a rectangular prism (assuming it is a rectangular prism): \[ V_A = \text{length} \times \text{width} \times \text{height} = 27.5 , \text{ft} \times 27.5 , \text{ft} \times 55 , \text{ft} \] Calculating this: \[ V_A = 27.5^2 \times 55 = 756.25 \times 55 = 41593.75 , \text{ft}^3 \]
Figure B:
- Dimensions: 5.5 ft, 5.5 ft, and 11 ft
- Volume \( V_B \): \[ V_B = 5.5 , \text{ft} \times 5.5 , \text{ft} \times 11 , \text{ft} \] Calculating this: \[ V_B = 5.5^2 \times 11 = 30.25 \times 11 = 332.75 , \text{ft}^3 \]
Ratio of the Volumes:
To find the ratio of the two volumes \( V_A \) and \( V_B \): \[ \text{Ratio} = \frac{V_A}{V_B} = \frac{41593.75}{332.75} \approx 125:1 \]
Since both Figure A and Figure B are rectangular prisms and their corresponding dimensions have a constant ratio of 5: 1 (since \( 27.5:5.5 = 5:1 \)), the figures are similar.
Conclusion:
Based on the calculations, the correct statement is: d. The two figures are similar because the volumes have a ratio of 125 : 1.
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