The problem asks to find the surface area of the label of a cylindrical can. The can has a diameter of 4 inches and a height of 6 inches. We need to find the area of the label, which is the lateral surface area of the cylinder, rounded to the nearest tenth.

1. Problem Description

The problem asks to find the surface area of the label of a cylindrical can. The can has a diameter of 4 inches and a height of 6 inches. We need to find the area of the label, which is the lateral surface area of the cylinder, rounded to the nearest tenth.

2. Solution Steps

The formula for the lateral surface area of a cylinder is:

$A = 2\pi r h$

Where $r$ is the radius and $h$ is the height. Since the diameter is 4 inches, the radius $r$ is half of that:

$r = \frac{4}{2} = 2$ inches

The height $h$ is given as 6 inches.

Substituting these values into the formula:

$A = 2\pi (2)(6)$

$A = 24\pi$

Now, we approximate $\pi$ as 3.14159 and calculate the area:

$A = 24 \times 3.14159$

$A = 75.39816$

We are asked to round the answer to the nearest tenth:

$A \approx 75.4$

3. Final Answer

The area of the label is approximately 75.4 square inches.