Question

What is the surface area of this cylinder?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

10 ft
7 ft

square feet

Answer 1

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

\[
\text{Surface Area} = 2\pi r(h + r)
\]

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

From your question:
- The height \( h = 10 \) ft
- The diameter is \( 7 \) ft, therefore the radius \( r = \frac{7}{2} = 3.5 \) ft.

Now, plug the values into the formula:

\[
\text{Surface Area} = 2\pi(3.5)(10 + 3.5)
\]

Calculating \( h + r \):

\[
h + r = 10 + 3.5 = 13.5
\]

Now substituting this back:

\[
\text{Surface Area} = 2\pi(3.5)(13.5)
\]

Now multiply it out:

\[
= 2 \times 3.14 \times 3.5 \times 13.5
\]

Calculating:

1. \( 3.5 \times 13.5 = 47.25 \)
2. \( 2 \times 3.14 = 6.28 \)
3. \( 6.28 \times 47.25 = 296.73 \)

Thus, the surface area of the cylinder is approximately:

\[
\text{Surface Area} \approx 296.73 \text{ square feet}
\]

Therefore, the surface area of the cylinder is **296.73 square feet**.