The area of a circle is given by the formula

a = Pi*r

We can solve for r:

a/Pi = r

√[a/Pi] = r (take the square root of both sides)

√[460/3.1416] = r (plug in the numbers)

√146.42 = r (evaluate)

12.1 = r

Check

Pi*r

3.1416*(12.1)

3.1416*146.41 = 460 (we note that 146.41 here is not the same as 146.42 above)

459.962 = 460 (We recognize that there is some error. This amount appears to be acceptable and unavoidable, given the precision of the math.)

a = Pi*r

^{2}(where "a" is the area, and "r" is the radius of the circle. Pi is an irrational number approximated by 3.1416.)We can solve for r:

a/Pi = r

^{2}(divide both sides by Pi)√[a/Pi] = r (take the square root of both sides)

√[460/3.1416] = r (plug in the numbers)

√146.42 = r (evaluate)

12.1 = r

Check

Pi*r

^{2}= 4603.1416*(12.1)

^{2}= 4603.1416*146.41 = 460 (we note that 146.41 here is not the same as 146.42 above)

459.962 = 460 (We recognize that there is some error. This amount appears to be acceptable and unavoidable, given the precision of the math.)