Identify Given Parameters

The radius of the base of the cylinder is given as $r = 7 \text{ cm}$ and the height is $h = 12 \text{ cm}$.

$r = 7 \text{ cm}, \quad h = 12 \text{ cm}$

Recall Total Surface Area Formula

The total surface area ($A$) of a solid cylinder includes the curved surface area and the areas of the two circular bases: $A = 2\pi rh + 2\pi r^2 = 2\pi r(r + h)$.

$A = 2\pi r(r + h)$

Substitute Values into the Formula

Substitute $r = 7$ and $h = 12$ into the formula: $A = 2 \times \pi \times 7 \times (7 + 12)$.

$A = 2 \times \pi \times 7 \times (19)$

Calculate the Final Area

Multiply the numbers: $2 \times 7 = 14$, and $14 \times 19 = 266$. Therefore, the total surface area is $266\pi \text{ cm}^2$.

$A = 266\pi \text{ cm}^2$