The surface area of the icing on the cake can be found by calculating the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
In this problem, the radius of the cake is 15 cm and the height of the cake is 12 cm. Therefore, the lateral surface area of the cake is:
Lateral Surface Area = 2π(15 cm)(12 cm)
Lateral Surface Area = 2π(180 cm²)
Lateral Surface Area = 360π cm²
Lateral Surface Area ≈ 1131 cm²
So, the amount of icing needed for one cake is approximately 1,131 square centimeters. However, we need to subtract the area of the circular bottom of the cake from this value. The area of the circular bottom of the cake is:
Area of circular bottom = πr²
Area of circular bottom = π(15 cm)²
Area of circular bottom = 225π cm²
Area of circular bottom ≈ 706.5 cm²
Therefore, the amount of icing needed for one cake is approximately:
1131 cm² - 706.5 cm² ≈ 424.5 cm²
Rounding this value to the nearest square centimeter, we get:
425 cm²
So, the answer is not listed. The amount of icing needed for one cake is approximately 425 square centimeters.