To determine the surface area of the cylinder using the given dimensions and formula, we will follow these steps:
1. Identify the given values: The radius [tex]\( r \)[/tex] is 8 inches and the height [tex]\( h \)[/tex] is 8 inches.
2. Recall the formula for the surface area of a cylinder:
[tex]\[
\text{Surface Area} = 2 \pi r h + 2 \pi r^2
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Surface Area} = 2 \pi (8) (8) + 2 \pi (8)^2
\][/tex]
4. Simplify the terms:
[tex]\[
2 \pi (8) (8) = 2 \pi \cdot 64 = 128 \pi
\][/tex]
[tex]\[
2 \pi (8)^2 = 2 \pi \cdot 64 = 128 \pi
\][/tex]
5. Add the simplified terms:
[tex]\[
128 \pi + 128 \pi = 256 \pi
\][/tex]
Therefore, the surface area of the cylinder is [tex]\( 256 \pi \)[/tex] square inches.
Hence, the correct answer is:
D. [tex]\( 256 \pi \)[/tex] in [tex]\( ^2 \)[/tex]
