Question

A cylinder has a height of 15 feet and a radius of 4 feet. Solve for the total surface area of the cylinder. Use 3.14 for pi and round to the nearest tenth. (1 point)

56.52 feet2

477.3 feet 2

301.44 feet

60 feet ^ 2

Answer 1

To find the total surface area of a cylinder, you can use the formula:

\[
\text{Total Surface Area} = 2\pi r^2 + 2\pi rh
\]

Where:
- \( r \) is the radius,
- \( h \) is the height.

Given:
- Height \( h = 15 \) feet,
- Radius \( r = 4 \) feet,
- Using \( \pi \approx 3.14 \).

Now, calculate each part of the formula step-by-step.

1. **Calculate the area of the two circular bases**:
\[
2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 100.48 \text{ feet}^2
\]

2. **Calculate the lateral surface area**:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 15 = 2 \times 3.14 \times 60 = 376.8 \text{ feet}^2
\]

3. **Add both areas to get the total surface area**:
\[
\text{Total Surface Area} = 100.48 + 376.8 = 477.28 \text{ feet}^2
\]

Now, round to the nearest tenth:
\[
\text{Total Surface Area} \approx 477.3 \text{ feet}^2
\]

Therefore, the total surface area of the cylinder is **477.3 feet²**.