#### Answer

The best estimate for the area of the face of a small coin is $6~cm^2$

#### Work Step by Step

Let the area of the coin be 6 units squared. We can find the radius $R$ of the coin.
$Area = \pi~R^2 = 6~units^2$
$R^2 = \frac{6~units^2}{\pi}$
$R = \sqrt{\frac{6~units^2}{\pi}}$
$R = 1.4~units$
For a small coin, a radius of 1.4 mm is too small and a radius of 1.4 dm is too large. A radius of 1.4 cm is the best estimate for the radius of a small coin.
The best estimate for the area of the face of a small coin is $6~cm^2$