The image shows two rectangular prisms (Figure 1 and Figure 2) with given dimensions, and the task involves calculating their volumes and the total volume.

Given Dimensions:

• Figure 1:
  • Length = 6 cm
  • Width = (not labeled but side "A")
  • Height = 7 cm
• Figure 2:
  • Length = 8 cm
  • Width = 3 cm
  • Height = 3 cm

Volumes:

• Volume of Figure 1: Since the dimensions of side A are missing, we will first need to find the volume of Figure 1. The volume of a rectangular prism is given by: $V = \text{Length} \times \text{Width} \times \text{Height}$ We know the volume is 42 cm³ (from the handwritten note). Using this, we can solve for the missing side "A".

• Volume of Figure 2: Using the formula for volume, and the dimensions for Figure 2: $V_2 = 8 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm} = 72 \, \text{cm}^3$

Total Volume:

$\text{Total Volume} = 42 \, \text{cm}^3 + 72 \, \text{cm}^3 = 114 \, \text{cm}^3$

Now, to find the missing side "A" in Figure 1, we use the volume of Figure 1: $V_1 = 6 \, \text{cm} \times A \times 7 \, \text{cm} = 42 \, \text{cm}^3$ $42 = 6 \times 7 \times A \quad \Rightarrow \quad A = \frac{42}{42} = 1 \, \text{cm}$

Thus, side A = 1 cm.

Would you like a more detailed explanation or have further questions? Here are some related questions:

1. How do you calculate the volume of irregular shapes composed of multiple prisms?
2. What is the formula for surface area for these prisms?
3. How does changing one dimension affect the volume?
4. What are the applications of volume calculations in real life?
5. Can the volume formula be applied to other 3D shapes like cylinders?

Tip: Always ensure that all dimensions are in the same unit before calculating the volume.