Question

The function A(r) = ar² gives the area of a circular object with respect to its radius r. Write the inverse

function r(A) to find the radius r required for area of A. Then estimate the radius of a circular object that
has an area of 40 cm²?

Answer 1

The inverse function r(A) for the area of a circular object is r = √(A/a). To estimate the radius with an area of 40 cm², use the equation r = √(A/a) and substitute A = 40.

Step-by-step explanation:

The inverse function r(A) can be found by solving the equation A = ar² for r. To do this, divide both sides of the equation by a and take the square root of both sides. This will give you the equation r = √(A/a). So the inverse function r(A) is r = √(A/a).

To estimate the radius of a circular object with an area of 40 cm², substitute A = 40 into the equation r = √(A/a) and solve for r. Since the value of a is not given, we cannot determine an exact value for r. However, you can approximate the value of a. For example, if the value of a = π, then r ≈ √(40/π).