Final answer:
The original area of the piece of tin is 1369 cm², which was calculated by solving for x after finding the dimensions of the box formed by the tin and applying the volume formula.
Step-by-step explanation:
The question pertains to finding the area of a piece of tin used to make a box with an open top by cutting out squares from each corner. The given volume of the box is 3249 cm³, and the size of the cut squares is 9 cm on each side. To find the original area, we will need to determine the size of the base of the box.
Let x be the side length of the original tin square. When a 9 cm square is cut from each corner, the new length and width of the box become (x - 18) cm (because 9 cm is removed from each side twice). The height of the box is 9 cm. The volume, V, of the box is given by V = length × width × height, which translates to 3249 cm³ = (x-18 cm) × (x-18 cm) × 9 cm. Solving this equation for x allows us to find the side length of the original piece of tin.
Simplifying the equation → 3249 cm³ = 9 cm × (x-18 cm) · (x-18 cm) → 361 cm² = (x-18 cm)² → x = 18 cm + 19 cm = 37 cm (applying square root to both sides). Now we can calculate the original area as A = x² = 37 cm × 37 cm = 1369 cm².