The Table A below shows the value of minerals exported by a country in the year 2010. Study and use it to answer the questions that follow.

The square root method for proportional circles means that the radius ($R$) is proportional to the square root of the value ($V$). So, $R = k \sqrt{V}$, where $k$ is a constant.
The given scale is 1 cm radius for 10 units of value. We use this to find $k$.

$$1 \text{ cm} = k \sqrt{10 \text{ units}}$$ $$k = \frac{1}{\sqrt{10}} \text{ cm/}\sqrt{\text{unit}}$$

Thus, the formula for the radius of each circle is $R = \frac{1}{\sqrt{10}} \sqrt{V} = \sqrt{\frac{V}{10}}$.

• For Rutile ($V = 196$ US Dollars):

$$R_{\text{Rutile}} = \sqrt{\frac{196}{10}} = \sqrt{19.6} \approx 4.43 \text{ cm}$$

• For Diamond ($V = 400$ US Dollars):

$$R_{\text{Diamond}} = \sqrt{\frac{400}{10}} = \sqrt{40} \approx 6.32 \text{ cm}$$

• For Bauxite ($V = 729$ US Dollars):

$$R_{\text{Bauxite}} = \sqrt{\frac{729}{10}} = \sqrt{72.9} \approx 8.54 \text{ cm}$$

• For Gold ($V = 900$ US Dollars):

$$R_{\text{Gold}} = \sqrt{\frac{900}{10}} = \sqrt{90} \approx 9.49 \text{ cm}$$

The radii for the proportional circles are:
Rutile: $\boxed{\text{4.43 cm}}$
Diamond: $\boxed{\text{6.32 cm}}$
Bauxite: $\boxed{\text{8.54 cm}}$
Gold: $\boxed{\text{9.49 cm}}$