Question

Question
A baker needs to cover a cylinder cake with icing. The cake has a radius of 5 inches and a height of 7 inches. How many square inches of icing will be needed to cover the sides and top of the cake? Icing will not be added to the bottom of the cake. Use 3.14 for pi and round your answer to the nearest tenth.

Answer 1

To calculate the amount of icing needed to cover the sides and top of a cylindrical cake, we need to find the surface area of both the side and the top of the cylinder.

1. **Surface Area of the Side (Lateral Area)**:
The lateral surface area \( A_{\text{side}} \) of a cylinder can be calculated using the formula:
\[
A_{\text{side}} = 2 \pi r h
\]
where \( r \) is the radius and \( h \) is the height.

Substituting the given values:
- Radius \( r = 5 \) inches
- Height \( h = 7 \) inches

\[
A_{\text{side}} = 2 \times 3.14 \times 5 \times 7
\]
\[
A_{\text{side}} = 2 \times 3.14 \times 35
\]
\[
A_{\text{side}} = 2 \times 109.9
\]
\[
A_{\text{side}} = 219.8 \text{ square inches}
\]

2. **Surface Area of the Top**:
The area of the top of the cylinder \( A_{\text{top}} \) can be calculated using the formula for the area of a circle:
\[
A_{\text{top}} = \pi r^2
\]

Substituting the value for the radius:
\[
A_{\text{top}} = 3.14 \times (5^2)
\]
\[
A_{\text{top}} = 3.14 \times 25
\]
\[
A_{\text{top}} = 78.5 \text{ square inches}
\]

3. **Total Surface Area for Icing**:
Now, we need to add the lateral area and the area of the top:
\[
A_{\text{total}} = A_{\text{side}} + A_{\text{top}}
\]
\[
A_{\text{total}} = 219.8 + 78.5
\]
\[
A_{\text{total}} = 298.3 \text{ square inches}
\]

Therefore, the total amount of icing needed to cover the sides and top of the cake is **298.3 square inches**.