To determine the surface area of a piece of pipe that is open at both ends with a radius of 6 inches and a height of 18 inches, we need to focus on the cylindrical part of the pipe. Since the pipe is open at both ends, we do not include the areas of the circular bases in our calculations, and only the lateral or curved surface area is considered.
Here are the detailed steps:
1. Determine the lateral surface area of the cylindrical part:
The formula to calculate the lateral surface area [tex]\( A_{\text{lateral}} \)[/tex] of a cylinder is:
[tex]\[
A_{\text{lateral}} = 2 \pi r h
\][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
- [tex]\( \pi \)[/tex] is approximately [tex]\( 3.14 \)[/tex]
Substitute the given values [tex]\( r = 6 \)[/tex] inches, [tex]\( h = 18 \)[/tex] inches, and [tex]\( \pi = 3.14 \)[/tex] into the formula:
[tex]\[
A_{\text{lateral}} = 2 \times 3.14 \times 6 \times 18
\][/tex]
2. Calculate the product:
First, multiply [tex]\( 2 \times 3.14 \)[/tex]:
[tex]\[
2 \times 3.14 = 6.28
\][/tex]
Next, multiply that result by the radius [tex]\( 6 \)[/tex]:
[tex]\[
6.28 \times 6 = 37.68
\][/tex]
Finally, multiply that result by the height [tex]\( 18 \)[/tex]:
[tex]\[
37.68 \times 18 = 678.24
\][/tex]
So, the lateral surface area of the pipe is [tex]\( 678.24 \)[/tex] square inches.
Since the pipe is open at both ends, the total surface area of the pipe is simply the lateral surface area.
Therefore, the surface area of the piece of pipe is:
[tex]\[
678.24 \, \text{in}^2
\][/tex]
The correct answer is:
[tex]\( 678.24 \, \text{in}^2 \)[/tex].
