The image contains questions regarding the volume and surface area of rectangular prisms. Let's solve the examples provided:

1) Volume Calculation:

The formula for the volume of a rectangular prism is:

$V = L \times W \times H$

For Figure 1:

• $L = 17 \, \text{cm}, \, W = 4 \, \text{cm}, \, H = 8 \, \text{cm}$ $V = 17 \times 4 \times 8 = 544 \, \text{cm}^3$

Correct calculation! The result is: $V = 544 \, \text{cm}^3$

2) Surface Area Calculation (Additional Work):

For a rectangular prism, the surface area (SA) formula is:

$SA = 2LW + 2LH + 2WH$

For Figure 1:

• $L = 17 \, \text{cm}, \, W = 4 \, \text{cm}, \, H = 8 \, \text{cm}$

$SA = 2(17 \cdot 4) + 2(17 \cdot 8) + 2(8 \cdot 4)$ $SA = 136 + 272 + 64 = 472 \, \text{cm}^2$

Correct calculation! The result is: $SA = 472 \, \text{cm}^2$

4) Volume and Surface Area Calculation:

For Figure 4:

• $L = 13 \, \text{m}, \, W = 7 \, \text{m}, \, H = 7 \, \text{m}$

Volume:

$V = L \times W \times H$ $V = 13 \times 7 \times 7 = 637 \, \text{m}^3$

Correct calculation! The result is: $V = 637 \, \text{m}^3$

Surface Area:

$SA = 2LW + 2LH + 2WH$ $SA = 2(13 \cdot 7) + 2(13 \cdot 7) + 2(7 \cdot 7)$ $SA = 182 + 182 + 98 = 462 \, \text{m}^2$

Correct calculation! The result is: $SA = 462 \, \text{m}^2$

Do you need detailed explanations for these formulas, or assistance with further calculations? 😊

5 Questions to Explore:

1. What is the physical significance of surface area versus volume in 3D shapes?
2. How does doubling one dimension affect the volume and surface area?
3. Can you derive the formula for the diagonal of a rectangular prism?
4. What are the real-life applications of calculating volume and surface area of rectangular prisms?
5. How would the formula change if the shape were a cylinder instead of a prism?

Tip:

Always include units in your final answers to ensure clarity and correctness in math problems!