Question

bisecting bakery sells cylindrical round cakes. the most popular cake at the bakery has a radius of 13 centimeters and a height of 15 centimeters.
if everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? use 3.14 for $pi$ and round to the nearest square centimeter.
$531\\ \text{cm}^2$
$612\\ \text{cm}^2$
$1,755\\ \text{cm}^2$
$2,286\\ \text{cm}^2$

Explanation:

Step1: Identify surface area components

We need the lateral surface area + area of 1 circular top (since the bottom is not iced).

Step2: Calculate lateral surface area

Formula: $2\pi rh$
$\text{Lateral Area} = 2 \times 3.14 \times 13 \times 15 = 1224.6 \, \text{cm}^2$

Step3: Calculate top circle area

Formula: $\pi r^2$
$\text{Top Area} = 3.14 \times 13^2 = 3.14 \times 169 = 530.66 \, \text{cm}^2$

Step4: Sum the two areas

Total icing area = Lateral Area + Top Area
$\text{Total Area} = 1224.6 + 530.66 = 1755.26 \, \text{cm}^2$

Step5: Round to nearest whole number

$1755.26 \approx 1755 \, \text{cm}^2$

Answer:

1,755 cm²