To find the total volume of the restaurant with the enclosed porch represented by the two rectangular prisms, we need to calculate the volume of each prism separately and then add them together.
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Volume of the larger rectangular prism:
- Length = 32 yards
- Height = 16 yards (given)
- Depth = 15 yards (total depth of both prisms is given as 15 yards; since the smaller prism's depth is 5 yards, the depth of the larger prism must be 15 - 5 = 10 yards)
Volume = Length × Height × Depth \[ \text{Volume}_{\text{larger}} = 32 , \text{yards} \times 16 , \text{yards} \times 10 , \text{yards} = 5120 , \text{yd}^3 \]
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Volume of the smaller rectangular prism:
- Length = 32 yards
- Height = 6 yards (given)
- Depth = 5 yards (given)
Volume = Length × Height × Depth \[ \text{Volume}_{\text{smaller}} = 32 , \text{yards} \times 6 , \text{yards} \times 5 , \text{yards} = 960 , \text{yd}^3 \]
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Total Volume of the restaurant: \[ \text{Total Volume} = \text{Volume}{\text{larger}} + \text{Volume}{\text{smaller}} = 5120 , \text{yd}^3 + 960 , \text{yd}^3 = 6080 , \text{yd}^3 \]
Thus, the total volume of the restaurant with the enclosed porch is \( 6080 , \text{yd}^3 \).
The correct answer is:
6,080 yd.³