Question

If the tin has a radius of 6 inches and a height of 4 inches, approximately what is the area of the surface to be covered with the butter mixture? Use 3.14 for and round to the nearest hundredth.

Answer 1

To calculate the surface area of a cylindrical tin, we need to consider both the lateral surface area and the areas of the two circular bases.

1. **Lateral Surface Area (A_lateral)**:
\[
A_{\text{lateral}} = 2\pi rh
\]
where \( r \) is the radius and \( h \) is the height.

2. **Area of the two bases (A_bases)**:
\[
A_{\text{bases}} = 2\pi r^2
\]
This is because there are two bases, each with an area of \( \pi r^2 \).

Now, let's calculate both parts using \( \pi \approx 3.14 \), \( r = 6 \) inches, and \( h = 4 \) inches.

### Step 1: Calculate the lateral surface area
\[
A_{\text{lateral}} = 2 \cdot 3.14 \cdot 6 \cdot 4
\]
\[
= 2 \cdot 3.14 \cdot 24
\]
\[
= 6.28 \cdot 24
\]
\[
= 150.72 \text{ square inches}
\]

### Step 2: Calculate the area of the two bases
\[
A_{\text{bases}} = 2 \cdot 3.14 \cdot 6^2
\]
\[
= 2 \cdot 3.14 \cdot 36
\]
\[
= 6.28 \cdot 36
\]
\[
= 226.08 \text{ square inches}
\]

### Step 3: Total surface area
Now sum the lateral area and the base area:
\[
A_{\text{total}} = A_{\text{lateral}} + A_{\text{bases}}
\]
\[
= 150.72 + 226.08
\]
\[
= 376.80 \text{ square inches}
\]

So, the total surface area to be covered with the butter mixture is approximately \( \boxed{376.80} \) square inches.