The radius of a circle is given as 2.12 cm . Its area must be...

The radius of the circle is given as $r = 2.12 \text{ cm}$.

The number of significant figures in the measured value of the radius is $3$.

The area of the circle is $A = \pi r^2$.

Substituting the value of $r$:

$A = \pi \times (2.12)^2 = 3.14159 \times 4.4944 = 14.1196... \text{ cm}^2$

In multiplication, the final result should retain as many significant figures as are there in the original number with the least significant figures. Since the radius has $3$ significant figures, the area must also be expressed to $3$ significant figures.

Rounding off $14.1196... \text{ cm}^2$ to $3$ significant figures, we get $14.1 \text{ cm}^2$.