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Question
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An illustration shows a rectangular prism, placed vertically, on the top corner of a larger cube. The length and width of the prism is 1 foot respectively and the height is 3 feet. The sides of the cube are 3 feet.

What is the volume of the composite figure?

(1 point)
ft.3

Answer 1

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

1. **Volume of the cube**:
The formula for the volume of a cube is given by:
\[
V = s^3
\]
where \( s \) is the length of a side. Given that the sides of the cube are 3 feet:
\[
V_{\text{cube}} = 3^3 = 27 \text{ ft}^3
\]

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. For the prism, given that its length and width are both 1 foot and its height is 3 feet:
\[
V_{\text{prism}} = 1 \times 1 \times 3 = 3 \text{ ft}^3
\]

3. **Total volume of the composite figure**:
Now we can add the volumes of the cube and the prism:
\[
V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}} = 27 \text{ ft}^3 + 3 \text{ ft}^3 = 30 \text{ ft}^3
\]

Thus, the volume of the composite figure is **30 ft³**.