Consider the 6-in by 9 inch rectangular cake that is two 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
you forgot about the top!
To calculate the surface area of the cake that will be covered with frosting, we need to find the surface area of the top and sides of the cake.
1. Start by finding the surface area of the top of the cake:
The top of the cake is a rectangle with dimensions 6 inches by 9 inches.
Surface area of the top = length × width = 6 in × 9 in = 54 square inches.
2. Next, find the surface area of the four sides of the cake:
Each side of the cake is a rectangle with dimensions 6 inches by 2 inches.
Surface area of one side = length × height = 6 in × 2 in = 12 square inches.
Since there are four sides, multiply the surface area of one side by 4.
Surface area of the four sides = 12 sq in × 4 = 48 square inches.
3. Add the surface area of the top and the four sides together:
Surface area covered with frosting = surface area of the top + surface area of the four sides
Surface area covered with frosting = 54 sq in + 48 sq in = 102 square inches.
Therefore, the surface area of the cake that will be covered with frosting is 102 square inches.
To find the surface area of the cake that will be covered with frosting, you need to calculate the combined area of the four sides and the top of the cake.
Firstly, let's calculate the area of the sides. A rectangular cake with dimensions 6 inches by 9 inches has two sides with dimensions 6 inches by 2 inches, and two sides with dimensions 9 inches by 2 inches. The area of each smaller side is calculated by multiplying the length and width, so:
Area of the first side = 6 inches × 2 inches = 12 square inches
Area of the second side = 6 inches × 2 inches = 12 square inches
Area of the third side = 9 inches × 2 inches = 18 square inches
Area of the fourth side = 9 inches × 2 inches = 18 square inches
Now, let's calculate the area of the top of the cake. The top has dimensions 6 inches by 9 inches, so:
Area of the top = 6 inches × 9 inches = 54 square inches
To find the total surface area covered with frosting, we sum up the areas of all the sides and top of the cake:
Total surface area covered with frosting = Area of the first side + Area of the second side + Area of the third side + Area of the fourth side + Area of the top
= 12 square inches + 12 square inches + 18 square inches + 18 square inches + 54 square inches
= 114 square inches
Therefore, the surface area of the cake that will be covered with frosting is 114 square inches.