To find the surface area of a cylinder, you can use the surface area formula for a cylinder:
[tex]\[ \text{Surface Area} = 2\pi r(h + r) \][/tex]
where [tex]\( r \)[/tex] is the base radius, and [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- The base radius [tex]\( r \)[/tex] is 3 inches.
- The height [tex]\( h \)[/tex] is 6 inches.
Let's substitute the given values into the formula and simplify step-by-step:
1. Identify [tex]\( r \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[
r = 3 \text{ in}, \quad h = 6 \text{ in}
\][/tex]
2. Substitute [tex]\( r \)[/tex] and [tex]\( h \)[/tex] into the surface area formula:
[tex]\[
\text{Surface Area} = 2\pi (3) \left(6 + 3\right)
\][/tex]
3. Simplify inside the parenthesis first:
[tex]\[
6 + 3 = 9
\][/tex]
4. Now substitute this value back into the formula:
[tex]\[
\text{Surface Area} = 2\pi (3) \times 9
\][/tex]
5. Multiply 3 by 9:
[tex]\[
3 \times 9 = 27
\][/tex]
6. Now substitute this value back into the formula:
[tex]\[
\text{Surface Area} = 2\pi \times 27
\][/tex]
7. Finally, multiply 2 by 27:
[tex]\[
2 \times 27 = 54
\][/tex]
8. Thus, the surface area in terms of [tex]\(\pi\)[/tex] is:
[tex]\[
\text{Surface Area} = 54\pi \text{ square inches}
\][/tex]
Therefore, the surface area of the cylinder is:
[tex]\[ 54\pi \text{ square inches} \][/tex]
