To find the answer, we must use the surface area to find the radius, and then double the radius to see if its within the acceptable range for the diameter.
The surface area of a circle can be found by this equation:
A = 4π (r²) , where A is surface area, and r is the radius.
Let's plug in 9π for A, and solve for the radius:
9π = 4π (r²) Divide both sides by 4π, the π's cancel out
9/4 = r²
Take the square root. Remember there's a square in the numerator and the denominator.
3/2 = r
r is equal to 3/2, or 1.5. Remember that the diameter is just the radius multiplied by 2.
d = 2r
d = (3/2) * 2 = 3
The diameter is 3, which is a bit higher than the range of regulation size. Therefore, the ball is not within range.
