Question

Find the surface area of a cylinder with a height of 7 ft and a base radius of 4 ft.
Use the value 3.14 for pi , and do not do any rounding.
Be sure to include the correct unit.

Answer 1

To find the surface area of a cylinder, we can use the following formula:

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

where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder

Given:
- Height (\( h \)) = 7 ft
- Radius (\( r \)) = 4 ft
- Use \( \pi = 3.14 \)

Now we can calculate the surface area step by step.

1. **Calculate the area of the two circular bases:**

\[
2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 2 \times 50.24 = 100.48 \, \text{ft}^2
\]

2. **Calculate the lateral surface area:**

\[
2\pi rh = 2 \times 3.14 \times 4 \times 7 = 2 \times 3.14 \times 28 = 2 \times 87.92 = 175.84 \, \text{ft}^2
\]

3. **Add both areas together to get the total surface area:**

\[
\text{Total Surface Area} = 100.48 + 175.84 = 276.32 \, \text{ft}^2
\]

Thus, the surface area of the cylinder is \( \boxed{276.32 \, \text{ft}^2} \).