Question

Use the image to answer the 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

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

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

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

6,080 yd.3

Answer 1

To find the total volume of the two rectangular prisms, we will calculate the volume of each prism separately and then add them together.

**Volume of a rectangular prism** is calculated using the formula:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

1. **Smaller Rectangular Prism**:
- Length = 32 yards
- Width (Depth) = 5 yards (as given)
- Height = 6 yards
- Volume = \( 32 \times 5 \times 6 = 960 \) cubic yards

2. **Larger Rectangular Prism**:
- Length = 32 yards
- Width (Depth) = 15 yards - 5 yards (depth of the smaller prism) = 10 yards
- Height = 16 yards
- Volume = \( 32 \times 10 \times 16 = 5,120 \) cubic yards

Now, add the volumes of the two prisms together:
\[
\text{Total Volume} = 960 + 5,120 = 6,080 \text{ cubic yards}
\]

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