Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the formula for calculating the area of a circle?

1. A = pi x r^2

2. C = 2 x pi x r

3. A = 2 x r

4. C = pi x d

The correct answer is: A = pi x r^2

The formula for calculating the area of a circle is A = πr², where A represents the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. This formula originated from the concept of filling a circle with infinitely small squares, and it derives from geometric principles concerning the relationship between the radius and the space the circle occupies. When you square the radius (r²), you are effectively scaling the area based on how far the radius extends from the center of the circle to its edge. The π in the formula serves as a ratio that relates the circle's diameter to its circumference, and it's integral to determining the area enclosed within the circumference. The other options do not describe the area: - The second option relates to the circumference of a circle, which is calculated using the formula C = 2πr. - The third option suggests a linear measurement, not representative of area, as it just multiplies the radius by 2. - The fourth option also refers to the circumference, but using diameter (d) instead of radius, as C = πd. Thus, only the formula A = πr² accurately conveys the means to calculate the area of