Final answer:
To find the area of the original piece of tin, calculate the dimensions of the open box created by cutting 9 cm squares from each corner. The area of the original piece of tin is 2601 cm^2.
Step-by-step explanation:
To find the area of the original piece of tin, we need to calculate the dimensions of the open box created.
Given that a square piece of tin is made into an open box by cutting a 9 cm square from each corner, the dimensions of the base of the box will be (x-18) cm by (x-18) cm, where x is the length of one side of the original piece of tin. The height of the box will be 9 cm.
Using the formula for the volume of a rectangular box, V = lwh, we have:
3249 cm^3 = ((x-18)*(x-18)*9) cm^3.
Simplifying and solving the equation gives x = 51 cm. The area of the original piece of tin is the square of the length of one side, which is (51*51) cm^2 = 2601 cm^2.