To find the total volume of the two rectangular prisms, we will calculate the volume of each prism separately and then sum them up.
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Volume of the Smaller Rectangular Prism:
- Length = 32 yards
- Height = 6 yards
- Depth = 5 yards
The volume \( V \) is given by the formula: \[ V = \text{Length} \times \text{Height} \times \text{Depth} \] So, for the smaller prism: \[ V_{\text{small}} = 32 , \text{yd} \times 6 , \text{yd} \times 5 , \text{yd} = 960 , \text{yd}^3 \]
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Volume of the Larger Rectangular Prism:
- Length = 32 yards
- Height = 16 yards
- The total combined depth is 15 yards, and since the smaller prism's depth is 5 yards, the larger prism's depth will be: \[ 15 , \text{yd} - 5 , \text{yd} = 10 , \text{yd} \]
Now calculating the volume for the larger prism: \[ V_{\text{large}} = 32 , \text{yd} \times 16 , \text{yd} \times 10 , \text{yd} = 5120 , \text{yd}^3 \]
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Total Volume: We add the volumes of the two prisms together: \[ V_{\text{total}} = V_{\text{small}} + V_{\text{large}} = 960 , \text{yd}^3 + 5120 , \text{yd}^3 = 6080 , \text{yd}^3 \]
Therefore, the total volume of the restaurant with an enclosed porch is 6,080 yd³.
The correct response is: 6,080 yd.³