In these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Radius find a function that models the radius r of a circle in term of its area A.

In these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Radius find a function that models the radius r of a circle in term of its area A.

Question
Modeling data distributions
asked 2021-02-04
In these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Radius find a function that models the radius r of a circle in term of its area A.

Answers (1)

2021-02-05

Concept used:
Area of circle is defined as,
\(\displaystyle{A}=\pi{x}^{{{2}}}\).....(1)
Here, A is area, x is radius of circle.
Calculation:
Consider the radius of circle is r.
Substitute r for x in equation (1) to obtain the model that express radius of circle.
\(\displaystyle{A}=\pi{r}^{{{2}}}\)
\(\displaystyle{\frac{{{A}}}{{\pi}}}={r}^{{{2}}}\)
\(\displaystyle{r}^{{{2}}}={\frac{{{A}}}{{\pi}}}\)
\(\displaystyle{r}=\sqrt{{{\frac{{{A}}}{{\pi}}}}}\)
Answer:
Thus, the function that models the radius of circle in terms of area is \(r=\sqrt{\frac{A}{\pi}}\)

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