Question

What is the volume of the composite figure?
U shaped figures broken into pieces.
Rectangular prism length 16in, width 7 in,height 7 in
Rectangular prism length 16in width 7 in,height 7 in.
And middle prism shows width 10 in and height 8 in

Answer 1

To find the volume of the composite U-shaped figure made up of the two identical rectangular prisms and the middle prism, we first need to calculate the volume of each component separately and then add them together.

1. **Volume of the first rectangular prism:**
The volume \( V \) of a rectangular prism is calculated as:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
For the first rectangular prism:
- Length = 16 inches
- Width = 7 inches
- Height = 7 inches

\[
V_1 = 16 \, \text{in} \times 7 \, \text{in} \times 7 \, \text{in} = 16 \times 49 = 784 \, \text{in}^3
\]

2. **Volume of the second rectangular prism:**
Since this is identical to the first rectangular prism, its volume is the same:
\[
V_2 = 784 \, \text{in}^3
\]

3. **Volume of the middle rectangular prism:**
For the middle prism:
- Width = 10 inches
- Height = 8 inches
- Length (same as the previous prisms) = 16 inches

\[
V_3 = 16 \, \text{in} \times 10 \, \text{in} \times 8 \, \text{in} = 16 \times 80 = 1280 \, \text{in}^3
\]

4. **Total Volume of the composite figure:**
Now, we add the volumes of the three components together:
\[
V_{\text{total}} = V_1 + V_2 + V_3 = 784 \, \text{in}^3 + 784 \, \text{in}^3 + 1280 \, \text{in}^3
\]
\[
V_{\text{total}} = 1568 \, \text{in}^3 + 1280 \, \text{in}^3 = 3848 \, \text{in}^3
\]

Therefore, the total volume of the composite U-shaped figure is **3848 cubic inches**.