Marco is baking a cake for a party. The cake is in the shape of a right circular cylinder. He needs to buy frosting for the cake but doesn’t know the surface area of the cake. If the diameter of the cake pan is 13 inches, and the height is 4 inches, what is the surface area he needs to frost? Use 3.14 for π .(1 point) Responses 428.61 inches2 428.61 inches squared 163.28 inches2 163.28 inches squared 265.33 inches2 265.33 inches squared 1,287.88 inches2
To find the surface area of the cake, we need to find the lateral surface area and then add the area of the two circular bases.
The lateral surface area of a cylinder can be calculated using the formula: 2πrh, where r is the radius and h is the height. Since we know the diameter is 13 inches, the radius is half of that, so the radius is 6.5 inches.
Therefore, the lateral surface area = 2 * 3.14 * 6.5 * 4 = 163.28 inches squared
To find the area of the two circular bases, we use the formula for the area of a circle: πr^2.
The area of one circular base = 3.14 * 6.5^2 = 132.665 inches squared
The area of both circular bases = 2 * 132.665 = 265.33 inches squared
Now, we add the lateral surface area and the area of the two circular bases:
163.28 + 265.33 = 428.61 inches squared
Therefore, Marco needs to frost a surface area of 428.61 inches squared.