Question

How do I calculate the surface area of a cylinder with a radius of 5 inches and a height of 8 inches?

Answer 1

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

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

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14159.

Given:
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 8 inches

Now, substitute the values into the formula:

\[
\text{Surface Area} = 2\pi(5)(8 + 5)
\]

First, calculate \( (8 + 5) \):

\[
8 + 5 = 13
\]

Now, substitute that back into the equation:

\[
\text{Surface Area} = 2\pi(5)(13)
\]

Now calculate \( 2 \times 5 \times 13 \):

\[
2 \times 5 = 10
\]
\[
10 \times 13 = 130
\]

So, now we have:

\[
\text{Surface Area} = 130\pi
\]

Now, to get a numerical value, multiply by \( \pi \):

\[
130 \times 3.14159 \approx 408.41
\]

Thus, the surface area of the cylinder is approximately \( 408.41 \) square inches.

So, the final answer is:

\[
\text{Surface Area} \approx 408.41 \text{ square inches}
\]