Question

problem 5b
explain how you know the relationship between the radius of a
circle and its area is not proportional.
use the table if it helps with your thinking

Explanation:

For a proportional relationship, the ratio of \( y \) to \( x \) (here \( y=\text{Area}, x = \text{Radius}\)) should be constant.

• When \( x = 1,y=3.14\), the ratio \(\frac{y}{x}=\frac{3.14}{1}=3.14\).
• When \( x = 2,y = 12.56\), the ratio \(\frac{y}{x}=\frac{12.56}{2}=6.28\).
• When \( x = 3,y=28.26\), the ratio \(\frac{y}{x}=\frac{28.26}{3}=9.42\).

Since the ratios \(\frac{\text{Area}}{\text{Radius}}\) are not the same ( \(3.14
eq6.28
eq9.42\)), the relationship between the radius of a circle and its area is not proportional.

Answer:

The relationship between the radius of a circle and its area is not proportional because the ratio of the area to the radius is not constant. For \(r = 1\), \(\frac{A}{r}=\frac{3.14}{1}=3.14\); for \(r = 2\), \(\frac{A}{r}=\frac{12.56}{2}=6.28\); for \(r = 3\), \(\frac{A}{r}=\frac{28.26}{3}=9.42\). Since \(3.14
eq6.28
eq9.42\), the ratio \(\frac{\text{Area}}{\text{Radius}}\) is not constant, so the relationship is non - proportional.