Question

Question
Adrian is painting the 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 paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are 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.(1 point)
ft2

Answer 1

To calculate the surface area of a cylinder, we need to find the combined area of the lateral surface and the top and bottom circular faces.

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

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

where:
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.

Given:
- \( r = 4 \) feet,
- \( h = 3 \) feet.

We can calculate each component step by step.

1. **Calculate the lateral surface area** \( (2\pi rh) \):
\[
2\pi rh = 2 \times 3.14 \times 4 \times 3
\]
\[
= 2 \times 3.14 \times 12
\]
\[
= 2 \times 37.68 = 75.36 \text{ square feet}
\]

2. **Calculate the area of the top and bottom faces** \( (2\pi r^2) \):
\[
2\pi r^2 = 2 \times 3.14 \times 4^2
\]
\[
= 2 \times 3.14 \times 16
\]
\[
= 2 \times 50.24 = 100.48 \text{ square feet}
\]

3. **Add the lateral surface area and the area of the top and bottom faces**:
\[
A = 75.36 + 100.48 = 175.84 \text{ square feet}
\]

Finally, rounding \( 175.84 \) to the nearest tenth, we get:

\[
\text{Surface area} \approx 175.8 \text{ square feet}
\]

Therefore, the surface area of the outside of the cylinder is **175.8 ft²**.