What formula is used to calculate the area of a circle?

What formula is used to calculate the area of a circle?

• A. A = l x w
• B. A = 3.14(r)^2
• C. A = 2πr
• D. A = 4/3πr^3

Answer: (B)

To calculate the area of a circle, the correct formula is based on the relationship between the radius of the circle and its area. The formula \( A = \pi r^2 \), which can be approximated using \( 3.14 \) for \( \pi \), indicates that the area \( A \) is directly proportional to the square of the radius \( r \). In this formula, the \( \pi \) (approximately 3.14) represents the ratio of the circumference of a circle to its diameter. Thus, as the radius increases, the area increases quadratically, meaning that even a small increase in the radius results in a significant increase in the area. This quadratic relationship is essential in understanding how circles grow in size. The other formulas refer to different geometrical properties: one calculates the area of a rectangle (length times width), one gives the circumference of a circle (2πr), and the last calculates the volume of a sphere (4/3πr³). Each of these serves a unique purpose in geometry, but only the area formula for a circle employs the radius in its squared form to yield the area. Therefore, \( A = 3.14(r)^2 \) is correctly

To calculate the area of a circle, the correct formula is based on the relationship between the radius of the circle and its area. The formula ( A = \pi r^2 ), which can be approximated using ( 3.14 ) for ( \pi ), indicates that the area ( A ) is directly proportional to the square of the radius ( r ).

In this formula, the ( \pi ) (approximately 3.14) represents the ratio of the circumference of a circle to its diameter. Thus, as the radius increases, the area increases quadratically, meaning that even a small increase in the radius results in a significant increase in the area. This quadratic relationship is essential in understanding how circles grow in size.

The other formulas refer to different geometrical properties: one calculates the area of a rectangle (length times width), one gives the circumference of a circle (2πr), and the last calculates the volume of a sphere (4/3πr³). Each of these serves a unique purpose in geometry, but only the area formula for a circle employs the radius in its squared form to yield the area. Therefore, ( A = 3.14(r)^2 ) is correctly