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.(1 point)

Answer 1

To find the total area of icing needed to cover the sides and the top of the cylindrical cake, we need to calculate the lateral surface area and the area of the top surface of the cylinder.

1. **Lateral Surface Area**:
The formula for the lateral surface area of a cylinder is:
\[
A_{lateral} = 2\pi rh
\]
where \( r \) is the radius and \( h \) is the height.

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

\[
A_{lateral} = 2 \times 3.14 \times 5 \times 7
\]

Calculating it step by step:
\[
A_{lateral} = 2 \times 3.14 \times 5 = 31.4
\]
\[
A_{lateral} = 31.4 \times 7 = 219.8 \text{ square inches}
\]

2. **Area of the Top Surface**:
The area of the top surface of the cylinder (which is a circle) is given by the formula:
\[
A_{top} = \pi r^2
\]

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

3. **Total Area of Icing Needed**:
The total area that needs icing is the sum of the lateral surface area and the top surface area:
\[
A_{total} = A_{lateral} + A_{top}
\]
\[
A_{total} = 219.8 + 78.5 = 298.3 \text{ square inches}
\]

Rounding to the nearest tenth, the total icing needed is:
\[
\boxed{298.3} \text{ square inches}
\]