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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

6,080 yd.3
6,080 yd. cubed

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

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

4,160 yd.3

Answer 1

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

1. Volume of the smaller rectangular prism:

   • Length = 32 yards
   • Height = 6 yards
   • Depth = 5 yards
   • Volume = Length × Height × Depth
   • Volume = 32 × 6 × 5 = 960 cubic yards

2. Volume of the larger rectangular prism:

   • Length = 32 yards
   • Height = 16 yards
   • Depth (calculated from combined depth, noting that the depth of the larger prism is the total depth minus the smaller prism's depth):
     • Total combined depth = 15 yards
     • Depth of larger prism = Total depth - Depth of smaller prism = 15 - 5 = 10 yards
   • Volume = Length × Height × Depth
   • Volume = 32 × 16 × 10 = 5120 cubic yards

3. Total volume of the restaurant:

   • Total Volume = Volume of smaller prism + Volume of larger prism
   • Total Volume = 960 + 5120 = 6080 cubic yards

Therefore, the total volume of the restaurant with the enclosed porch is 6,080 yd³.

So the correct response is: 6,080 yd.³