Question
An illustration shows a cube with a smaller rectangular prism attached to the bottom right side. The sides of the cube are of 5 feet. The prism 1.5 feet long and 2 feet high.
What is the volume of the composite figure?
(1 point)
Responses
128 ft.3
128 ft. cubed
136.25 ft.3
136.25 ft. cubed
140 ft.3
140 ft. cubed
155 ft.3
What is the volume of the composite figure?
(1 point)
Responses
128 ft.3
128 ft. cubed
136.25 ft.3
136.25 ft. cubed
140 ft.3
140 ft. cubed
155 ft.3
Answers
GPT-4o mini
To find the volume of the composite figure (the cube plus the rectangular prism), we must first calculate the volume of each individual shape.
1. **Volume of the Cube**:
The formula for the volume \( V \) of a cube is given by:
\[
V = s^3
\]
where \( s \) is the length of a side of the cube. Here, \( s = 5 \) feet.
\[
V_{\text{cube}} = 5^3 = 125 \text{ ft}^3
\]
2. **Volume of the Rectangular Prism**:
The formula for the volume \( V \) of a rectangular prism is given by:
\[
V = l \times w \times h
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height. In this case, the prism is 1.5 feet long, with a width of 5 feet (the same as the side of the cube), and a height of 2 feet.
\[
V_{\text{prism}} = 1.5 \times 5 \times 2 = 15 \text{ ft}^3
\]
3. **Total Volume of the Composite Figure**:
Now, we can find the total volume by adding the volumes of the cube and the rectangular prism together:
\[
V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}} = 125 \text{ ft}^3 + 15 \text{ ft}^3 = 140 \text{ ft}^3
\]
Therefore, the volume of the composite figure is **140 ft³**.
So the correct response is:
**140 ft cubed**.
1. **Volume of the Cube**:
The formula for the volume \( V \) of a cube is given by:
\[
V = s^3
\]
where \( s \) is the length of a side of the cube. Here, \( s = 5 \) feet.
\[
V_{\text{cube}} = 5^3 = 125 \text{ ft}^3
\]
2. **Volume of the Rectangular Prism**:
The formula for the volume \( V \) of a rectangular prism is given by:
\[
V = l \times w \times h
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height. In this case, the prism is 1.5 feet long, with a width of 5 feet (the same as the side of the cube), and a height of 2 feet.
\[
V_{\text{prism}} = 1.5 \times 5 \times 2 = 15 \text{ ft}^3
\]
3. **Total Volume of the Composite Figure**:
Now, we can find the total volume by adding the volumes of the cube and the rectangular prism together:
\[
V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}} = 125 \text{ ft}^3 + 15 \text{ ft}^3 = 140 \text{ ft}^3
\]
Therefore, the volume of the composite figure is **140 ft³**.
So the correct response is:
**140 ft cubed**.