The formula for the area of a circle is:
\[
\text{Area} = \pi r^2
\]
Given that the radius \( r = 7 \, \text{cm} \), we can substitute the value into the formula:
\[
\text{Area} = \pi \times (7)^2 = 49\pi \, \text{cm}^2
\]
Thus, the area of the circle is \( 49\pi \, \text{cm}^2 \). Therefore, the correct answer is option (1).