Adrian is painting that outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to put paint all around the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface area of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.

To find the total surface area of a cylinder, we need to calculate the surface area of the lateral side and the areas of the two circular bases (top and bottom).

The formula for the surface area \( A \) of a cylinder is given by:

\[ A = 2\pi r h + 2\pi r^2 \]

Where:

• \( r \) is the radius of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is a constant (~3.14).

Given:

• Radius \( r = 4 \) feet,
• Height \( h = 3 \) feet.

First, we calculate the lateral surface area:

\[ \text{Lateral Surface Area} = 2\pi r h = 2 \times 3.14 \times 4 \times 3 \] Calculating this step-by-step:

1. Calculate \( 2 \times 3.14 = 6.28 \).
2. Multiply by the radius \( 4 \): \( 6.28 \times 4 = 25.12 \).
3. Multiply by the height \( 3 \): \( 25.12 \times 3 = 75.36 \).

So, the lateral surface area is \( 75.36 \) square feet.

Next, we calculate the area of the two bases:

\[ \text{Area of Two Bases} = 2\pi r^2 = 2 \times 3.14 \times (4^2) \] Calculating \( 4^2 \):

\[ 4^2 = 16 \]

Calculating the area:

1. Calculate \( 2 \times 3.14 = 6.28 \).
2. Multiply by the area of one base \( 16 \): \( 6.28 \times 16 = 100.48 \).

So, the area of the two bases is \( 100.48 \) square feet.

Now, we add the lateral surface area and the area of the two bases:

\[ \text{Total Surface Area} = 75.36 + 100.48 = 175.84 \text{ square feet} \]

Finally, rounding to the nearest tenth:

\[ \text{Total Surface Area} \approx 175.8 \text{ square feet} \]

Thus, the surface area of the cylinder is \( \boxed{175.8} \) square feet.