Priya is making a four-layered wedding cake. Her cake is in the shape of a cylinder with a radius of 6 inches. Each layer has a height of 2 inches. What is the total surface area of Priya’s four cake layers, before stacking? Use 3.14 for π and round to the nearest hundredth
To calculate the total surface area of Priya's four cake layers, we first need to find the surface area of one cake layer and then multiply it by 4.
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
Where:
r = radius = 6 inches
h = height of one cake layer = 2 inches
Plugging in the values, we get:
Lateral Surface Area = 2 * 3.14 * 6 * 2
Lateral Surface Area = 75.36 square inches
Since there are two circular surfaces on each cake layer, we need to also calculate the area of a circle and then multiply it by 2.
The formula for the surface area of a circle is given by:
Surface Area of a Circle = πr^2
Plugging in the values, we get:
Surface Area of a Circle = 3.14 * 6^2
Surface Area of a Circle = 113.04 square inches
So, the total surface area of one cake layer is:
Total Surface Area of One Cake Layer = Lateral Surface Area + 2 * Surface Area of a Circle
Total Surface Area of One Cake Layer = 75.36 + 2 * 113.04
Total Surface Area of One Cake Layer = 301.44 square inches
Finally, to find the total surface area of all four cake layers, we multiply the total surface area of one cake layer by 4:
Total Surface Area = 301.44 * 4
Total Surface Area = 1205.76 square inches
Therefore, the total surface area of Priya's four cake layers, before stacking, is approximately 1205.76 square inches.