1. **State the problem:** We need to find the difference in volume between two cubes built by Hector and Karin with side lengths 12 in. and 14 in. respectively. 2. **Formula for volume of a cube:** The volume $V$ of a cube with side length $s$ is given by: $$V = s^3$$ 3. **Calculate Hector's cube volume:** $$V_H = 12^3 = 12 \times 12 \times 12 = 1728$$ cubic inches 4. **Calculate Karin's cube volume:** $$V_K = 14^3 = 14 \times 14 \times 14 = 2744$$ cubic inches 5. **Find the difference in volume:** $$\text{Difference} = V_K - V_H = 2744 - 1728 = 1016$$ cubic inches 6. **Explanation:** The difference in volume is $1016$ cubic inches, meaning Karin's cube contains $1016$ more 1-inch cubes than Hector's cube. --- 1. **State the problem:** Mr. Williams wants to give one eraser to each of his 365 students. Each eraser is 1 cubic inch. We need to check if one box of erasers is enough. 2. **Given:** The box dimensions are not explicitly given, but from the problem context, assume the box volume equals the number of erasers it contains. 3. **Calculate the box volume:** Since each eraser is 1 cubic inch, the number of erasers equals the box volume in cubic inches. 4. **Compare erasers needed and box capacity:** If the box volume (number of erasers) is at least 365, Mr. Williams has enough erasers. 5. **Conclusion:** If the box volume is less than 365, he does not have enough erasers. Since the problem does not provide the box volume, we cannot definitively answer without that information. --- **Final answers:** - Difference in volume between cubes: $1016$ cubic inches. - For the erasers, more information about the box volume is needed to answer.