Final answer:
To cover 11 sheet cakes with icing on the top and sides, approximately 4.76 gallons of icing are needed. This is calculated by finding the surface area that needs icing and dividing it by the area covered by one cup of icing, then converting cups to gallons.
Step-by-step explanation:
To calculate the gallons of icing needed for the 11 sheet cakes, first determine the total surface area that needs to be covered with icing. Since icing is being applied to both the top and sides of each cake, we'll calculate the area for each and add them up.
Area of the top of one cake:
30 inches (length) x 20 inches (width) = 600 square inches
Perimeter of one cake:
(30 inches + 20 inches) x 2 = 100 inches
Area of the sides of one cake:
100 inches (perimeter) x 2 inches (height) = 200 square inches
Total area for one cake:
600 inches (top) + 200 inches (sides) = 800 square inches
Total area for 11 cakes:
800 square inches x 11 = 8800 square inches
Now, we use the given information that one cup of icing spreads over 115.5 square inches. To find out how many cups are needed for 8800 square inches:
Cups of icing needed:
8800 square inches ÷ 115.5 square inches per cup = approximately 76.19 cups
Since there are 16 cups in a gallon, we convert the cups to gallons:
Gallons of icing needed:
76.19 cups ÷ 16 cups per gallon = approximately 4.76 gallons
Therefore, about 4.76 gallons of icing are needed to cover the 11 sheet cakes.