Correct Response: B. The area of a circle can be calculated using the equation, a = π r2, where a represents the area, r represents the radius, and π is a specific irrational number. In this problem, the original area equals 144 π square feet, and the final area equals 576 π square feet. The factor requested can be found by dividing the final area by the original area, yielding (576 π)/(144 π) = 4. In general, if a quantity is directly proportional to the square of particular variable, and the value of the variable is multiplied by a factor of x, the resulting quantity will increase by a factor of x2. Answer choice (A) is reached by assuming that a doubling of the radius would result in a doubling of the area. Answer choice (C) is reached by assuming that the scale factor (4) should be cubed. This would have been correct for the volume of a spherical object. Answer choice (D) is reached by assuming that an increase of 12 in the radius will increase the area by the same amount.
