Question
What is the volume of the composite figure?
Shows rectangular prism with a cube on top..
Length of prism is 11 in,height 4 in. Cube is 3in width and 3in height
Shows rectangular prism with a cube on top..
Length of prism is 11 in,height 4 in. Cube is 3in width and 3in height
Answers
GPT-4o mini
To find the volume of the composite figure (a rectangular prism with a cube on top), you need to calculate the volume of each shape individually and then add them together.
1. **Volume of the rectangular prism**:
- Volume formula: \( V = \text{length} \times \text{width} \times \text{height} \)
- Given length = 11 inches, width = (which is not given but assumed based on the cube's width), and height = 4 inches.
- Since the cube on top has a width of 3 inches, we can assume this width is the width of the prism as well, making it a rectangular prism with a width of 3 inches.
\[
V_{\text{prism}} = 11 \, \text{in} \times 3 \, \text{in} \times 4 \, \text{in} = 132 \, \text{in}^3
\]
2. **Volume of the cube**:
- Volume formula: \( V = \text{side}^3 \)
- Given side of the cube = 3 inches.
\[
V_{\text{cube}} = 3 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in} = 27 \, \text{in}^3
\]
3. **Total volume of the composite figure**:
- Add the volumes of the prism and the cube together.
\[
V_{\text{total}} = V_{\text{prism}} + V_{\text{cube}} = 132 \, \text{in}^3 + 27 \, \text{in}^3 = 159 \, \text{in}^3
\]
Therefore, the volume of the composite figure is **159 cubic inches**.
1. **Volume of the rectangular prism**:
- Volume formula: \( V = \text{length} \times \text{width} \times \text{height} \)
- Given length = 11 inches, width = (which is not given but assumed based on the cube's width), and height = 4 inches.
- Since the cube on top has a width of 3 inches, we can assume this width is the width of the prism as well, making it a rectangular prism with a width of 3 inches.
\[
V_{\text{prism}} = 11 \, \text{in} \times 3 \, \text{in} \times 4 \, \text{in} = 132 \, \text{in}^3
\]
2. **Volume of the cube**:
- Volume formula: \( V = \text{side}^3 \)
- Given side of the cube = 3 inches.
\[
V_{\text{cube}} = 3 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in} = 27 \, \text{in}^3
\]
3. **Total volume of the composite figure**:
- Add the volumes of the prism and the cube together.
\[
V_{\text{total}} = V_{\text{prism}} + V_{\text{cube}} = 132 \, \text{in}^3 + 27 \, \text{in}^3 = 159 \, \text{in}^3
\]
Therefore, the volume of the composite figure is **159 cubic inches**.