Calculate and compare the volume of the two figures in the image. Choose which statement is true. Figure a is H = 27.5 ft L = 55 ft and W = 27.5 ft. Figure B is H = 5.5 ft. W = 5.5 ft. and W = 11 ft. (1 point) Responses The two figures are similar because the volumes have a ratio of 5 : 1 . The two figures are similar because the volumes have a ratio of ratio of 5 to 1 . The two figures are similar because the volumes have a ratio of 125 : 1 . The two figures are similar because the volumes have a ratio of ratio of 125 to 1 . The two figures are not similar because there is no scale factor stated for the volume. The two figures are not similar because there is no scale factor stated for the volume. The two figures are not similar because the volumes are not the same.

Answer 1

To determine the correct statement regarding the volumes of Figure A and Figure B, we first need to calculate the volumes of both figures.

Figure A:

• Dimensions:

  • Height (H) = 27.5 ft
  • Length (L) = 55 ft
  • Width (W) = 27.5 ft

• Volume of Figure A (V_A) is calculated using the formula for the volume of a rectangular prism:
  \[ V_A = H \times L \times W = 27.5 \times 55 \times 27.5 \]

\[ V_A = 27.5 \times 55 \times 27.5 = 27.5^2 \times 55 = 756.25 \times 55 = 41,593.75 \text{ ft}^3 \]

Figure B:

• Dimensions:

  • Height (H) = 5.5 ft
  • Width (W) = 5.5 ft
  • Length (L) = 11 ft

• Volume of Figure B (V_B) is calculated using the same volume formula:
  \[ V_B = H \times L \times W = 5.5 \times 11 \times 5.5 \]

\[ V_B = 5.5 \times 11 \times 5.5 = 5.5^2 \times 11 = 30.25 \times 11 = 332.75 \text{ ft}^3 \]

Now that we have both volumes:

• Volume of Figure A \( V_A = 41,593.75 \text{ ft}^3 \)
• Volume of Figure B \( V_B = 332.75 \text{ ft}^3 \)

Next, we can find the ratio of their volumes: \[ \text{Volume Ratio} = \frac{V_A}{V_B} = \frac{41,593.75}{332.75} \approx 125 : 1 \]

This means the volumes of the two figures have a ratio of 125:1.

Now we can compare the statements:

1. The two figures are similar because the volumes have a ratio of 5 : 1.
2. The two figures are similar because the volumes have a ratio of ratio of 5 to 1.
3. The two figures are similar because the volumes have a ratio of 125 : 1.
4. The two figures are similar because the volumes have a ratio of ratio of 125 to 1.
5. The two figures are not similar because there is no scale factor stated for the volume.
6. The two figures are not similar because the volumes are not the same.

Based on our calculations, the true statements are:

• "The two figures are similar because the volumes have a ratio of 125 : 1" (3)
• "The two figures are similar because the volumes have a ratio of ratio of 125 to 1" (4)

Both statements 3 and 4 are correct, but if we are to choose only one, either one works. However, since they are worded slightly differently, choose option 3 for clarity.

Final answer: The true statement is "The two figures are similar because the volumes have a ratio of 125 : 1."