Consider the 6 inch x 9 inch rectangular cake that is 2 inches deep. If you cover the cake with frosting excluding the bottom, what is the surface area of the cake that will be covered with frosting?

Answer 1

First, let's find the surface area of one side of the cake. The cake has dimensions of 6 inches by 9 inches, so the surface area of one side is:

6 inches x 9 inches = 54 square inches

Since there are two sides to cover with frosting (top and sides), we need to find the total surface area of both sides. The top side has an area of:

6 inches x 9 inches = 54 square inches

The two side faces are rectangles with dimensions of:

2 inches x 6 inches = 12 square inches
2 inches x 9 inches = 18 square inches

Adding up the areas of both side faces:

12 square inches + 18 square inches = 30 square inches

Now we can add the surface area of both sides to find the total surface area that will be covered with frosting:

54 square inches (top) + 30 square inches (sides) = 84 square inches

Therefore, the surface area of the cake that will be covered with frosting is 84 square inches.