Question

Jared baked a cake for his sister's birthday and is trying to figure out how much frosting he will need to decorate it. The cake has a diameter of 20 cm
and a height of 8 cm
.

If he only wants to frost the top and the sides of the cake, how much frosting will he need? Use pi = 3.14
.

Area to be frosted

Answer 1

To calculate the area that Jared needs to frost, we need to find the surface area of the top of the cake and the lateral surface area of the sides. The cake is a cylinder, so we can use the following formulas:

1. **Area of the top (circular area)**:
\[
\text{Area}_{\text{top}} = \pi r^2
\]
where \( r \) is the radius.

2. **Lateral surface area (side area)**:
\[
\text{Area}_{\text{sides}} = 2 \pi r h
\]
where \( h \) is the height of the cake.

Given:
- Diameter of the cake = 20 cm, so the radius \( r \) is:
\[
r = \frac{\text{diameter}}{2} = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]
- Height \( h = 8 \, \text{cm} \)

Now let's calculate each area:

### 1. Area of the top
\[
\text{Area}_{\text{top}} = \pi r^2 = 3.14 \times (10 \, \text{cm})^2 = 3.14 \times 100 \, \text{cm}^2 = 314 \, \text{cm}^2
\]

### 2. Lateral surface area
\[
\text{Area}_{\text{sides}} = 2 \pi r h = 2 \times 3.14 \times 10 \, \text{cm} \times 8 \, \text{cm}
\]
\[
= 2 \times 3.14 \times 10 \times 8 = 3.14 \times 160 = 502.4 \, \text{cm}^2
\]

### Total area to be frosted
Now, we add the area of the top and the lateral surface area:
\[
\text{Total Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{sides}} = 314 \, \text{cm}^2 + 502.4 \, \text{cm}^2 = 816.4 \, \text{cm}^2
\]

Therefore, the total area that Jared will need to frost is **816.4 cm²**.