Answer:
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. Since we know that the circular region has an area of 90π square feet, we can set this equal to the area formula and solve for r:
A = πr^2
90π = πr^2
90 = r^2
Taking the square root of both sides, we get:
r = √90
r = √(9 x 10)
r = 3√10
The diameter of the circle is equal to twice the radius, so we have:
d = 2r
d = 2(3√10)
d = 6√10
Therefore, the diameter of the circle is 6√10 feet.