To calculate the surface area of a closed cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- \( r = 2 \) inches,
- \( h = 5 \) inches.
Now we can substitute these values into the formula:
\[ \text{Surface Area} = 2\pi(2)(5 + 2) \]
Calculating the height plus radius:
\[ 5 + 2 = 7 \]
Now substitute that back in:
\[ \text{Surface Area} = 2\pi(2)(7) \]
Calculate \( 2 \times 2 \times 7 \):
\[ 2 \times 2 = 4, \] \[ 4 \times 7 = 28. \]
So, the surface area is:
\[ \text{Surface Area} = 28\pi \text{ square inches}. \]
Thus, the answer is:
D. \( 28\pi \) inches\(^2\).