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Question

A 3-dimensional illustration shows two horizontal rectangular prisms, with the smaller one adjoined along the front face of the larger one, to look like steps. Edges that are not visible are drawn with dashed lines. The rectangular prism in front is smaller than the one in the back. The length of both the prisms is 32 yards. The smaller rectangular prism is 6 yards high and 5 yards deep. The larger rectangular prism is 16 yards high. The total combined depth of the two prisms is 15 yards.

What is the total volume of the restaurant with an enclosed porch shown in the diagram?

(1 point)
Responses

8,640 yd.3
8,640 yd. cubed

5,070 yd.3
5,070 yd. cubed

4,160 yd.3
4,160 yd. cubed

6,080 yd.3
6,080 yd. cubed
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Answer 1

To find the total volume of the restaurant with the enclosed porch, we need to calculate the volumes of both the larger and smaller rectangular prisms and then add them together.

1. Volume of the larger rectangular prism:

• Length = 32 yards
• Height = 16 yards
• Depth = Total depth - Depth of the smaller prism = 15 yards - 5 yards = 10 yards

Volume = Length × Height × Depth

Volume of the larger prism = 32 yards × 16 yards × 10 yards = 5,120 cubic yards

2. Volume of the smaller rectangular prism:

• Length = 32 yards
• Height = 6 yards
• Depth = 5 yards

Volume of the smaller prism = Length × Height × Depth

Volume of the smaller prism = 32 yards × 6 yards × 5 yards = 960 cubic yards

3. Total volume of the restaurant:

Total Volume = Volume of the larger prism + Volume of the smaller prism

Total Volume = 5,120 cubic yards + 960 cubic yards = 6,080 cubic yards

Thus, the total volume of the restaurant with an enclosed porch is:

6,080 yd³ (6,080 cubic yards).