The area of the square as a function of radius is given as A(r) = 2r^2
As given in the question a square is inscribed in a b. So the diagonals of the square will be the diameter of the circle.
The formula for the diagonals of the square is,
D = s√2
Where, s = side of the square
And the formula for the diameter of the circle is,
D = 2r
Where r = radius of the circle
As, Diagonals of the square = Diameter of the circle
Thus, s√2 = 2r
s = 2r/√2
s = r√2 (1)
Now, the formula of the area of the square is,
A = s^2
Putting the value of s from equation (1) in the above formula we get
A = (r√2)^2
A = 2r^2
Hence the area of the square as a function of radius is given as A(r) = 2r^2
Learn more about area of square here : brainly.com/question/25092270
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