Final answer:
To find the surface area of the cheesecake pan, multiply the dimensions of the pan and calculate the area of each face. Then, add up the areas of all the faces to find the total surface area.
Step-by-step explanation:
To find the surface area of a cheesecake baked in this pan, we need to find the total area of all the faces of the pan. The pan is in the shape of a rectangular prism, so it has 6 faces: 2 rectangular faces with dimensions 8 inches by 12 inches, and 4 rectangular faces with dimensions 8 inches by the height of the pan.
The volume of the pan is given as 288 cubic inches. The volume of a rectangular prism is found by multiplying the length, width, and height of the prism. We can use this information to find the height of the pan:
288 = 8 x 12 x height
Solving for height, we have:
height = 288 / (8 x 12) = 3 inches
Now we can calculate the surface area of the cheesecake pan:
The surface area = 2(8x12) + 4(8x3) = 192 + 96 = 288 square inches