Question

Figure A
27.5 ft.
27.5 ft.
55 ft.

Figure B
5.5 ft.
5.5 ft.
11 ft.

Calculate and compare the volume of the two figures in the image. Choose which statement is true.

a. The two figures are similar because there is no scale factor stated for the volume
b. The two figures are similar because the volumes have a ratio of 5 : 1.
c. The two figures are not similar because the volumes are not the same
d. The two figures are similar because the volumes have a ratio of 125 : 1.

Answer 1

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.**