Question

Find the surface area of the cylinder.
Radius: 3 yd
Height: 4 yd

Answer 1

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

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

where \( r \) is the radius and \( h \) is the height of the cylinder. In this case, the radius \( r \) is 3 yards and the height \( h \) is 4 yards.

Plugging the values into the formula:

\[
\text{Surface Area} = 2\pi (3)(4 + 3)
\]

First, calculate \( h + r \):

\[
h + r = 4 + 3 = 7
\]

Now substitute it back into the formula:

\[
\text{Surface Area} = 2\pi (3)(7)
\]

Calculating it step by step:

\[
\text{Surface Area} = 2\pi (21) = 42\pi
\]

To get a numerical value, we can use \( \pi \approx 3.14 \):

\[
\text{Surface Area} \approx 42 \times 3.14 \approx 131.88
\]

Thus, the surface area of the cylinder is:

\[
\text{Surface Area} \approx 131.88 \text{ square yards}
\]

For a more exact answer, we can leave it as:

\[
\text{Surface Area} = 42\pi \text{ square yards}
\]