We know the area of the circle is given by pi*r^2. And the diameter is 2*r.
Now the area of the circle is 201.1 in^2.
Therefore 201.1 = pi*r^2
=> r^2 = 201.1 / pi
=> r^2 = 64.0 (approximately)
=> r = sqrt 64
=> r = 8
Diameter = 2*r = 2*8 = 16
Therefore the required diameter is 16 in.
Given the area of a circle = 201.1 in^2.
We need to find the length of the diameter of the circle.
We will use the area of a circle formula to find the radius.
We know that:
The area of the circle = r^2 * pi where r is the radius.
Let us substitute.
==> A = r^2 *pi
==> 201.1 = r^2 *pi
Now we will divide by pi.
==> r^2 = 201.1/ pi = 64.01
==> r= 8 ( approx.)
Then the radius of the circle is 8 in.
But we know that the diameter is twice the radius.
==> The diameter = 2* r = 2*8 = 16
Then, the length of the diameter = 16 in.
Let the diameter of the circle be 2r and radius r.
Then the area of the circle = pir^2 .
The actual area of the circle = 201.1 in^2.
Therefore pir^2 = 201.1.
Therefore r^2 = 201.1/pi/
=> r = sqrt(201.1/pi).
So the diameter of the circle = 2r = 2sqrt(201.1/pi) = 16.00 inch nearly.