Question

A cake has a radius of 5 in and a height of 7 in How amny sqaure in of icing will be needed to covor the sides and top of the cake us 3.14 as pi and round your answer to thenearest tenth

Answer 1

To find the amount of icing needed to cover the sides and top of a cylindrical cake, we will calculate the surface area of the cylinder (which consists of the lateral area and the area of the top face).

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

2. **Area of the Top Face**:
The formula for the area \( A_{\text{top}} \) of the top face of the cylinder is:
\[
A_{\text{top}} = \pi r^2
\]

3. **Total Surface Area**:
The total surface area \( A_{\text{total}} \) that needs icing will be the sum of the lateral surface area and the area of the top face:
\[
A_{\text{total}} = A_{\text{lateral}} + A_{\text{top}}
\]

Now let’s calculate each component:

### Step 1: Calculate the Lateral Surface Area
Given:
- \( r = 5 \) inches
- \( h = 7 \) inches

\[
A_{\text{lateral}} = 2 \times 3.14 \times 5 \times 7
\]
\[
A_{\text{lateral}} = 2 \times 3.14 \times 35
\]
\[
A_{\text{lateral}} = 6.28 \times 35
\]
\[
A_{\text{lateral}} = 219.8 \text{ square inches}
\]

### Step 2: Calculate the Area of the Top Face
\[
A_{\text{top}} = 3.14 \times (5^2)
\]
\[
A_{\text{top}} = 3.14 \times 25
\]
\[
A_{\text{top}} = 78.5 \text{ square inches}
\]

### Step 3: Calculate the Total Surface Area
\[
A_{\text{total}} = 219.8 + 78.5
\]
\[
A_{\text{total}} = 298.3 \text{ square inches}
\]

Finally, rounding to the nearest tenth, the total amount of icing needed to cover the sides and top of the cake is:
\[
\boxed{298.3} \text{ square inches}
\]