An open box is made from a square piece of cardboard 48 inches on a side by cutting identical squares from the comers and turning up the sides. Use this information to complete parts a through c Find and interpret \( \mathrm{V}(10) \) Seloct the correct choice below and, if necessary, fill in the answer box to complete your choice (Simplity your answer Type an integer or a decimal) A. The volume of the box \( \mathrm{V}(10) \) is piece of cardboard is 10 inches. B. The volume of the box \( \mathrm{V}(10) \) is center of each edge of the piece of cardboard is 10 inches. C. The volume of the box \( \mathrm{V}(10) \) is of the square cut from each comer of the of the piece of cardboard is inches, when the side of the square cut from the center of each edge D. The volume of the box \( \mathrm{V}(10) \) is ? cubic inches, when the side of the square cut from the center of the piece of cardboard is 10 inches.

To find the volume of the box when 10-inch squares are cut from each corner, let's set up the equation. After cutting 10-inch squares, the new dimensions of the box will be \( 48 - 2(10) = 28 \) inches for the length and width, and the height will be 10 inches. Thus, the volume \( V \) can be calculated as: \[ V = \text{length} \times \text{width} \times \text{height} = 28 \times 28 \times 10. \] Calculating this gives: \[ V = 28 \times 28 = 784 \quad \text{then} \quad 784 \times 10 = 7840. \] So, the volume of the box \( V(10) \) is 7840 cubic inches. Now, let's interpret our choices: A. The volume of the box \( V(10) \) is when the side of the square cut from each corner of the piece of cardboard is 10 inches. B. The volume of the box \( V(10) \) is 7840 cubic inches. C. The volume of the box \( V(10) \) is when 10-inch squares are cut from the corners. D. The volume of the box \( V(10) \) is 7840 cubic inches. In this case, option D fits just right, as it directly states the volume calculated!