The image contains two problems involving the volume and surface area of rectangular prisms. Let’s analyze and verify the calculations step-by-step.

Problem 1

Given Dimensions:

• Length ($L$) = 15 cm
• Width ($W$) = 3 cm
• Height ($H$) = 12 cm

Volume Calculation

Formula for the volume of a rectangular prism: $V = L \times W \times H$

Substitute the given values: $V = 15 \times 3 \times 12 = 540 \, \text{cm}^3$ Volume: $540 \, \text{cm}^3$

Surface Area Calculation

Formula for the surface area ($SA$) of a rectangular prism: $SA = 2(LW + LH + WH)$

Substitute the given values: $SA = 2[(15 \times 3) + (15 \times 12) + (3 \times 12)]$ $SA = 2[45 + 180 + 36]$ $SA = 2 \times 261 = 522 \, \text{cm}^2$ Surface Area: $522 \, \text{cm}^2$

Problem 2

Given Dimensions:

• Length ($L$) = 9 m
• Width ($W$) = 14 m
• Height ($H$) = 6 m

Volume Calculation

Formula for the volume: $V = L \times W \times H$

Substitute the given values: $V = 9 \times 14 \times 6 = 756 \, \text{m}^3$ Volume: $756 \, \text{m}^3$

Surface Area Calculation

Formula for the surface area ($SA$): $SA = 2(LW + LH + WH)$

Substitute the given values: $SA = 2[(9 \times 14) + (9 \times 6) + (14 \times 6)]$ $SA = 2[126 + 54 + 84]$ $SA = 2 \times 264 = 528 \, \text{m}^2$ Surface Area: $528 \, \text{m}^2$

Verifications

1. The provided answers for both volume and surface area are correct based on the calculations.

Would you like further clarification or details?
Here are 5 questions related to the problems above:

1. What is the general method for finding the surface area of a prism with more complex shapes?
2. How can you convert volume units from cubic meters to cubic centimeters?
3. What are the practical applications of calculating surface area and volume?
4. How do you calculate the diagonal length of a rectangular prism?
5. What happens to the surface area if all dimensions are doubled?

Tip: Always double-check units when solving geometry problems to ensure consistency!