To solve the problem of finding the volume of each rectangular prism, we need to count the number of unit cubes in each figure. The volume of a rectangular prism is given by the formula:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
However, since each figure is composed of unit cubes (where each cube represents \(1 \, \text{ft}^3\)), we can simply count the total number of cubes in each figure.
Let's go through each figure step by step:
Figure 1:
-
Shape: A rectangular prism with dimensions \(4 \times 3 \times 2\).
-
Calculation: \(4 \times 3 \times 2 = 24\).
-
Volume: \(24 \, \text{ft}^3\).
Figure 2:
-
Shape: A rectangular prism with dimensions \(5 \times 3 \times 2\).
-
Calculation: \(5 \times 3 \times 2 = 30\).
-
Volume: \(30 \, \text{ft}^3\).
Figure 3:
-
Shape: A cube with dimensions \(3 \times 3 \times 3\).
-
Calculation: \(3 \times 3 \times 3 = 27\).
-
Volume: \(27 \, \text{ft}^3\).
Figure 4:
-
Shape: A rectangular prism with dimensions \(3 \times 2 \times 2\).
-
Calculation: \(3 \times 2 \times 2 = 12\).
-
Volume: \(12 \, \text{ft}^3\).
Figure 5:
-
Shape: A rectangular prism with dimensions \(4 \times 3 \times 2\).
-
Calculation: \(4 \times 3 \times 2 = 24\).
-
Volume: \(24 \, \text{ft}^3\).
Figure 6:
-
Shape: A rectangular prism with dimensions \(4 \times 3 \times 3\).
-
Calculation: \(4 \times 3 \times 3 = 36\).
-
Volume: \(36 \, \text{ft}^3\).
Figure 7:
-
Shape: A rectangular prism with dimensions \(5 \times 2 \times 2\).
-
Calculation: \(5 \times 2 \times 2 = 20\).
-
Volume: \(20 \, \text{ft}^3\).
Figure 8:
-
Shape: A rectangular prism with dimensions \(3 \times 3 \times 4\).
-
Calculation: \(3 \times 3 \times 4 = 36\).
-
Volume: \(36 \, \text{ft}^3\).
Figure 9:
-
Shape: A cube with dimensions \(3 \times 3 \times 3\).
-
Calculation: \(3 \times 3 \times 3 = 27\).
-
Volume: \(27 \, \text{ft}^3\).
Final Answers:
\[
\begin{aligned}
1) & \quad 24 \, \text{ft}^3 \\
2) & \quad 30 \, \text{ft}^3 \\
3) & \quad 27 \, \text{ft}^3 \\
4) & \quad 12 \, \text{ft}^3 \\
5) & \quad 24 \, \text{ft}^3 \\
6) & \quad 36 \, \text{ft}^3 \\
7) & \quad 20 \, \text{ft}^3 \\
8) & \quad 36 \, \text{ft}^3 \\
9) & \quad 27 \, \text{ft}^3 \\
\end{aligned}
\]
\boxed{
\begin{array}{ccc}
24 & 30 & 27 \\
12 & 24 & 36 \\
20 & 36 & 27 \\
\end{array}
}
Parent Tip: Review the logic above to help your child master the concept of volume rectangular prisms worksheet.
