Question

An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long.
What is the volume of the composite figure?

(1 point)
in.3

Answer 1

To find the volume of the composite figure made up of three rectangular prisms, we will calculate the volume of each individual prism and then sum them up.

1. **Volume of the side rectangular prisms:**
Each side rectangular prism has dimensions:
- Length = 16 inches
- Width = 7 inches
- Height = 7 inches

The volume \(V\) of a rectangular prism is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

For each side prism:
\[
V = 16 \times 7 \times 7 = 16 \times 49 = 784 \text{ cubic inches}
\]

Since there are two identical side prisms:
\[
\text{Total volume of side prisms} = 2 \times 784 = 1568 \text{ cubic inches}
\]

2. **Volume of the center rectangular prism:**
The center rectangular prism has dimensions:
- Length = 10 inches
- Width = 8 inches
- Height = 7 inches (assuming it is the same height as the side prisms)

For the center prism:
\[
V = 10 \times 8 \times 7 = 80 \times 7 = 560 \text{ cubic inches}
\]

3. **Total volume of the composite figure:**
Now, we add the volumes of the side prisms and the center prism:
\[
\text{Total volume} = \text{Volume of side prisms} + \text{Volume of center prism}
\]
\[
= 1568 + 560 = 2128 \text{ cubic inches}
\]

Thus, the volume of the composite figure is \(\boxed{2128}\) cubic inches.