To solve the problem of finding the total volume of each figure, we need to break down each shape into simpler rectangular prisms and calculate their volumes individually. Then, we sum the volumes of these prisms to get the total volume for each figure.
Step-by-Step Solution:
####
Figure 1:
- The figure can be divided into two rectangular prisms:
1. A larger prism with dimensions \(5 \times 3 \times 7\).
2. A smaller prism with dimensions \(3 \times 3 \times 3\).
-
Volume of the larger prism:
\[
V_1 = 5 \times 3 \times 7 = 105 \, \text{cm}^3
\]
-
Volume of the smaller prism:
\[
V_2 = 3 \times 3 \times 3 = 27 \, \text{cm}^3
\]
-
Total volume:
\[
V_{\text{total}} = V_1 + V_2 = 105 + 27 = 132 \, \text{cm}^3
\]
####
Figure 2:
- The figure is a single rectangular prism with dimensions \(5 \times 4 \times 7\).
-
Volume:
\[
V = 5 \times 4 \times 7 = 140 \, \text{cm}^3
\]
####
Figure 3:
- The figure can be divided into two rectangular prisms:
1. A larger prism with dimensions \(4 \times 3 \times 9\).
2. A smaller prism with dimensions \(4 \times 1 \times 5\).
-
Volume of the larger prism:
\[
V_1 = 4 \times 3 \times 9 = 108 \, \text{cm}^3
\]
-
Volume of the smaller prism:
\[
V_2 = 4 \times 1 \times 5 = 20 \, \text{cm}^3
\]
-
Total volume:
\[
V_{\text{total}} = V_1 + V_2 = 108 + 20 = 128 \, \text{cm}^3
\]
####
Figure 4:
- The figure can be divided into two rectangular prisms:
1. A larger prism with dimensions \(4 \times 2 \times 5\).
2. A smaller prism with dimensions \(2 \times 2 \times 2\).
-
Volume of the larger prism:
\[
V_1 = 4 \times 2 \times 5 = 40 \, \text{cm}^3
\]
-
Volume of the smaller prism:
\[
V_2 = 2 \times 2 \times 2 = 8 \, \text{cm}^3
\]
-
Total volume:
\[
V_{\text{total}} = V_1 + V_2 = 40 + 8 = 48 \, \text{cm}^3
\]
####
Figure 5:
- The figure can be divided into two rectangular prisms:
1. A larger prism with dimensions \(3 \times 2 \times 7\).
2. A smaller prism with dimensions \(3 \times 3 \times 5\).
-
Volume of the larger prism:
\[
V_1 = 3 \times 2 \times 7 = 42 \, \text{cm}^3
\]
-
Volume of the smaller prism:
\[
V_2 = 3 \times 3 \times 5 = 45 \, \text{cm}^3
\]
-
Total volume:
\[
V_{\text{total}} = V_1 + V_2 = 42 + 45 = 87 \, \text{cm}^3
\]
####
Figure 6:
- The figure can be divided into two rectangular prisms:
1. A larger prism with dimensions \(5 \times 2 \times 9\).
2. A smaller prism with dimensions \(3 \times 2 \times 5\).
-
Volume of the larger prism:
\[
V_1 = 5 \times 2 \times 9 = 90 \, \text{cm}^3
\]
-
Volume of the smaller prism:
\[
V_2 = 3 \times 2 \times 5 = 30 \, \text{cm}^3
\]
-
Total volume:
\[
V_{\text{total}} = V_1 + V_2 = 90 + 30 = 120 \, \text{cm}^3
\]
Final Answers:
\[
\boxed{132, 140, 128, 48, 87, 120}
\]
Parent Tip: Review the logic above to help your child master the concept of additive volume worksheet.
