Question

Use the image to answer the question.

An illustration shows a rectangular prism with a cube placed on top. The cube is 3 inches on all sides. The rectangular prism is 11 inches long and 4 inches high.

What is the volume of the composite figure?

(1 point)
in.3

Answer 1

To find the volume of the composite figure, we need to calculate the volumes of both the rectangular prism and the cube, and then sum them.

1. **Volume of the Cube:**
The formula for the volume of a cube is:
\[
V = s^3
\]
where \(s\) is the side length.

For the cube with a side length of 3 inches:
\[
V_{\text{cube}} = 3^3 = 27 \text{ cubic inches}
\]

2. **Volume of the Rectangular Prism:**
The formula for the volume of a rectangular prism is:
\[
V = l \times w \times h
\]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

The dimensions given are:
- Length (\(l\)) = 11 inches
- Width (\(w\)) = (Since it isn't explicitly provided, let's assume the width is necessary for volume calculation. We will denote it as \(w\)).
- Height (\(h\)) = 4 inches

Thus, the volume of the rectangular prism can be expressed as:
\[
V_{\text{prism}} = 11 \times w \times 4
\]
Without the width, we cannot compute a specific volume for the prism.

Assuming we assume or find that width to be given as well or solve it through other means, we will carry on assuming \( w = 4 \) as a placeholder.

\[
V_{\text{prism}} = 11 \times 4 \times 4 = 176 \text{ cubic inches}
\]

3. **Total Volume of the Composite Figure:**
Now we can sum the volumes of both the cube and the rectangular prism.
\[
V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}}
\]
Assuming \( w = 4 \):
\[
V_{\text{total}} = 27 + 176 = 203 \text{ cubic inches}
\]

Thus, the answer is:
\[
\text{Total Volume} = 203 \text{ in}^3
\]

If any width information changes, please update it, and we will adjust the height accordingly.