Question

The function f ( r ) = π r 2 determines the area of a circle in cm2, A , in terms of the radius of the circle in cm, r . Define a function g that determines the radius of a circle in cm, r , in terms of the area of the cirlce in cm2, A .

Answer 1

Answer:

$f(A)=\sqrt{\frac{A}{\pi} }$

Step-by-step explanation:

The function to find the area of the circle is

$f(r)=\pi r^2$

we need to frame equation for the radius of the circle in terms of area

Lets replace f(r) by A  

$A=\pi r^2$

Solve the given equation for 'r'

To solve for 'r' , divide both sides by pi

then take square root on both sides

$A=\pi r^2\\\\\frac{A}{\pi} =r^2\\\sqrt{\frac{A}{\pi} }=r\\ r=\sqrt{\frac{A}{\pi} }$

Now replace 'r' with f(A), the radius in terms of the area of the circle

$f(A)=\sqrt{\frac{A}{\pi} }$

Answer 2

Here we must define a function that determines the radius of a circle in terms of the area of the circle.

The function is g(A) = √(A/π).

We know that:

f(r) = π*r^2

Defines the area as a function of r, then we can write:

A = π*r^2

Isolating r we get:

r = √(A/π)

Then the function:

g(A) = √(A/π)

Determines the radius as a function of A, the area of the circle.

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