Volume Worksheets - Free Printable

Problem Overview:

The task involves calculating the total volume of joined rectangular prisms. Each figure is composed of two or more rectangular prisms, and we need to find the volume of each individual prism and then sum them up to get the total volume.

Solution Explanation:

#### Step 1: Understand the Volume Formula
The volume \( V \) of a rectangular prism is calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

#### Step 2: Analyze Each Figure

##### Figure 1:
- The figure consists of two rectangular prisms.
- Prism 1: Dimensions are \( 6 \times 5 \times 7 \).
\[
V_1 = 6 \times 5 \times 7 = 210 \, \text{cm}^3
\]
- Prism 2: Dimensions are \( 5 \times 5 \times 2 \).
\[
V_2 = 5 \times 5 \times 2 = 50 \, \text{cm}^3
\]
- Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 210 + 50 = 260 \, \text{cm}^3
\]

##### Figure 2:
- The figure consists of two rectangular prisms.
- Prism 1: Dimensions are \( 8 \times 8 \times 6 \).
\[
V_1 = 8 \times 8 \times 6 = 384 \, \text{cm}^3
\]
- Prism 2: Dimensions are \( 9 \times 2 \times 1 \).
\[
V_2 = 9 \times 2 \times 1 = 18 \, \text{cm}^3
\]
- Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 384 + 18 = 402 \, \text{cm}^3
\]

##### Figure 3:
- The figure consists of two rectangular prisms.
- Prism 1: Dimensions are \( 10 \times 9 \times 8 \).
\[
V_1 = 10 \times 9 \times 8 = 720 \, \text{cm}^3
\]
- Prism 2: Dimensions are \( 8 \times 2 \times 1 \).
\[
V_2 = 8 \times 2 \times 1 = 16 \, \text{cm}^3
\]
- Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 720 + 16 = 736 \, \text{cm}^3
\]

##### Figure 4:
- The figure consists of two rectangular prisms.
- Prism 1: Dimensions are \( 5 \times 10 \times 5 \).
\[
V_1 = 5 \times 10 \times 5 = 250 \, \text{cm}^3
\]
- Prism 2: Dimensions are \( 2 \times 8 \times 3 \).
\[
V_2 = 2 \times 8 \times 3 = 48 \, \text{cm}^3
\]
- Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 250 + 48 = 298 \, \text{cm}^3
\]

##### Figure 5:
- The figure consists of two rectangular prisms.
- Prism 1: Dimensions are \( 10 \times 9 \times 8 \).
\[
V_1 = 10 \times 9 \times 8 = 720 \, \text{cm}^3
\]
- Prism 2: Dimensions are \( 5 \times 9 \times 1 \).
\[
V_2 = 5 \times 9 \times 1 = 45 \, \text{cm}^3
\]
- Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 720 + 45 = 765 \, \text{cm}^3
\]

Final Answer:

\[
\boxed{260 \, \text{cm}^3, 402 \, \text{cm}^3, 736 \, \text{cm}^3, 298 \, \text{cm}^3, 765 \, \text{cm}^3}
\]