Question

What is the surface area of this cylinder?

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

14 yd
8 yd

square yards

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 cylinder,
- \( h \) is the height of the cylinder.

From your information:
- The height \( h = 14 \) yd,
- The diameter is \( 8 \) yd, so the radius \( r = \frac{8}{2} = 4 \) yd.

Now, substituting these values into the surface area formula:

\[
\text{Surface Area} = 2 \pi (4)(14 + 4)
\]

Calculating \( 14 + 4 \):

\[
14 + 4 = 18
\]

Now substituting back into the surface area formula:

\[
\text{Surface Area} = 2 \pi (4)(18)
\]

Calculating \( 2 \times 4 \times 18 \):

\[
2 \times 4 = 8
\]
\[
8 \times 18 = 144
\]

Now substitute \( \pi \approx 3.14 \):

\[
\text{Surface Area} \approx 144 \times 3.14
\]

Calculating \( 144 \times 3.14 \):

\[
144 \times 3.14 = 452.16
\]

Therefore, the surface area of the cylinder, rounded to the nearest hundredth, is:

\[
\text{Surface Area} \approx 452.16 \text{ square yards}
\]