Question

What is the surface area of this cylinder?

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

9 yd
6 yd

square yards

Answer 1

To calculate 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.

Given:
- The diameter of the cylinder is 6 yards, so the radius \( r \) is \( \frac{6}{2} = 3 \) yards.
- The height \( h \) of the cylinder is 9 yards.

Now, plug in the values:

\[
\text{Surface Area} = 2\pi(3)(9 + 3)
\]

Calculate \( (9 + 3) \):

\[
= 12
\]

Now substitute that back into the equation:

\[
\text{Surface Area} = 2\pi(3)(12)
\]

Calculating \( 2 \times 3 \times 12 \):

\[
= 72
\]

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

\[
\text{Surface Area} = 72 \times 3.14
\]

Now perform the multiplication:

\[
72 \times 3.14 = 226.08
\]

Finally, round to the nearest hundredth:

The surface area of the cylinder is approximately **226.08 square yards**.