Step 1: Build the total surface area from its two pieces separately, instead of quoting the combined $3\pi r^2$ formula straight away.
A solid hemisphere has exactly two surfaces you can actually touch: the rounded outer shell, and the flat circular base where it would sit on a table. We will find the area of each one on its own and then add them.
Step 2: Convert the given diameter into a radius.
The diameter is given as $'2d'$. Since radius is always half the diameter:
\[ r = \frac{2d}{2} = d \]
Step 3: Find the curved (rounded) surface area on its own.
The curved surface of a hemisphere is exactly half the curved surface of a full sphere, which is $4\pi r^2$, so the curved part alone is:
\[ \text{Curved Surface Area} = 2\pi r^2 = 2\pi d^2 \]
Step 4: Find the flat circular base area on its own.
The flat base is just a circle of radius $r$, so its area is:
\[ \text{Base Area} = \pi r^2 = \pi d^2 \]
Step 5: Add the two pieces to get the total surface area.
\[ \text{TSA} = \text{Curved Surface Area} + \text{Base Area} = 2\pi d^2 + \pi d^2 = 3\pi d^2 \]
Step 6: Final answer.
The total surface area of the solid hemisphere is $3\pi d^2$, which is option (A).
\[ \boxed{3\pi d^2} \]