To accurately calculate and compare the volumes of the two figures, we first need to identify what shapes they represent, as the details provided involve dimensions that could fit various figures.
Here’s a breakdown based on the given dimensions:
Figure A
- Dimensions: 27.5 ft x 27.5 ft x 55 ft
- Assuming Figure A is a rectangular prism (or box), the volume \( V \) can be calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] Thus: \[ V_A = 27.5 , \text{ft} \times 27.5 , \text{ft} \times 55 , \text{ft} \] Calculating that: \[ V_A = 27.5 \times 27.5 \times 55 = 41,312.5 , \text{ft}^3 \]
Figure B
- Dimensions: 5.5 ft x 5.5 ft x 11 ft
- Assuming Figure B is also a rectangular prism, we use the same volume formula: \[ V_B = \text{length} \times \text{width} \times \text{height} \] Thus: \[ V_B = 5.5 , \text{ft} \times 5.5 , \text{ft} \times 11 , \text{ft} \] Calculating that: \[ V_B = 5.5 \times 5.5 \times 11 = 335.75 , \text{ft}^3 \]
Comparison
Now we can compare the volumes of the two figures:
- Volume of Figure A: 41,312.5 ft³
- Volume of Figure B: 335.75 ft³
Conclusion
Figure A has a significantly larger volume than Figure B. If presented with statements regarding the volume comparisons (e.g., "Figure A has a greater volume than Figure B"), that statement would indeed be true based on the calculations made.