To solve the problem of finding the volume of each composite figure, we need to break each figure into simpler shapes (rectangular prisms) and calculate their volumes individually. Then, we sum the volumes of these simpler shapes to get the total volume of the composite figure.
Problem 1:
The figure consists of two rectangular prisms stacked on top of each other.
-
Bottom Prism:
- Dimensions: \(4 \, \text{in} \times 2 \, \text{in} \times 3 \, \text{in}\)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 3 = 24 \, \text{in}^3
\]
-
Top Prism:
- Dimensions: \(1 \, \text{in} \times 2 \, \text{in} \times 1 \, \text{in}\)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 1 \times 2 \times 1 = 2 \, \text{in}^3
\]
-
Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{top}} = 24 + 2 = 26 \, \text{in}^3
\]
Problem 2:
The figure is a single rectangular prism with dimensions given directly.
-
Dimensions:
- Length: \(14 \, \text{cm}\)
- Width: \(12 \, \text{cm}\)
- Height: \(2 \, \text{cm}\)
-
Volume:
\[
V = \text{length} \times \text{width} \times \text{height} = 14 \times 12 \times 2 = 336 \, \text{cm}^3
\]
Problem 3:
The figure consists of two rectangular prisms placed side by side.
-
Left Prism:
- Dimensions: \(6 \, \text{in} \times 1 \, \text{in} \times 1 \, \text{in}\)
- Volume:
\[
V_{\text{left}} = \text{length} \times \text{width} \times \text{height} = 6 \times 1 \times 1 = 6 \, \text{in}^3
\]
-
Right Prism:
- Dimensions: \(8 \, \text{in} \times 3 \, \text{in} \times 1 \, \text{in}\)
- Volume:
\[
V_{\text{right}} = \text{length} \times \text{width} \times \text{height} = 8 \times 3 \times 1 = 24 \, \text{in}^3
\]
-
Total Volume:
\[
V_{\text{total}} = V_{\text{left}} + V_{\text{right}} = 6 + 24 = 30 \, \text{in}^3
\]
Problem 4:
The figure consists of two rectangular prisms placed end-to-end.
-
Left Prism:
- Dimensions: \(12 \, \text{ft} \times 4 \, \text{ft} \times 4 \, \text{ft}\)
- Volume:
\[
V_{\text{left}} = \text{length} \times \text{width} \times \text{height} = 12 \times 4 \times 4 = 192 \, \text{ft}^3
\]
-
Right Prism:
- Dimensions: \(8 \, \text{ft} \times 4 \, \text{ft} \times 4 \, \text{ft}\)
- Volume:
\[
V_{\text{right}} = \text{length} \times \text{width} \times \text{height} = 8 \times 4 \times 4 = 128 \, \text{ft}^3
\]
-
Total Volume:
\[
V_{\text{total}} = V_{\text{left}} + V_{\text{right}} = 192 + 128 = 320 \, \text{ft}^3
\]
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. & 26 \, \text{in}^3 \\
2. & 336 \, \text{cm}^3 \\
3. & 30 \, \text{in}^3 \\
4. & 320 \, \text{ft}^3 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of volume of composite figures worksheet.
