Question

A regulation baseball must have a diameter between 2.87 and 2.94 inches. The surface area of a particular baseball is 9π square inches. Is the baseball within the range of regulation size? Explain your answer.

Answer 1

Sample Response: The baseball is not regulation size. If the baseball has a surface area of 9π, then I can set that equal to the formula 4πr2 and solve for r. The radius is 3/2 inches, so I double that to find the diameter. The diameter of the ball is 3 inches, which is greater than the allowed range of diameters.

Answer 2

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.