divide the radius by Pi2
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The area of a circle is (pi)(r^2). Set this equal to 64 and solve for the radius. r = sqrt(64/pi)
Solve the equation for the area of the circle (area = pi x radius2) for radius. Multiply the radius by 2 to obtain the diameter.
-- Take the formula for the area of the circle in terms of the radius . . . A = (pi) R2-- Solve that formula for 'R'. You'll then have a formula for the radius in terms of the area,which is exactly what you're looking for.
You can certainly express the radius as a function of its area, yes. If the area is known, you can solve the formula for the area of the circle to uniquely get the radius. (The quadratic equation has two solutions; you will of course choose the positive solution for the radius.)
Pi can be used to solve many different things, such as the circumference, radius, diameter, or area of a circle, and the volume of a sphere.