What is the formula for the area of a circle?

What is the formula for the area of a circle?

• A. Pi x Diameter
• B. (2 x Pi) x Radius
• C. Pi x Radius^2
• D. Pi x Height

Answer: (C)

The area of a circle is calculated using the formula Pi times the square of the radius. This is represented mathematically as \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius of the circle. This formula derives from the relationship between a circle's radius and the space contained within the circle's boundary. When you square the radius, it effectively accounts for the two-dimensional nature of the circle, allowing for a measure of the entire area enclosed. The constant Pi (approximately 3.14159) is essential in calculations involving circles, as it relates the circumference of a circle to its diameter. To contrast, the other choices do not represent the area of a circle. For instance, multiplying Pi by the diameter provides a value related to the circumference, not the area. Similarly, multiplying (2 times Pi) by the radius is more related to the calculation of the circumference of a circle than its area. Lastly, using Pi times height refers to the formula for the volume of a cylinder and does not pertain to circles at all. Thus, the correct answer, Pi times Radius squared, accurately represents how to calculate the area of a circle.

The area of a circle is calculated using the formula Pi times the square of the radius. This is represented mathematically as ( A = \pi r^2 ), where ( A ) is the area and ( r ) is the radius of the circle. This formula derives from the relationship between a circle's radius and the space contained within the circle's boundary.

When you square the radius, it effectively accounts for the two-dimensional nature of the circle, allowing for a measure of the entire area enclosed. The constant Pi (approximately 3.14159) is essential in calculations involving circles, as it relates the circumference of a circle to its diameter.

To contrast, the other choices do not represent the area of a circle. For instance, multiplying Pi by the diameter provides a value related to the circumference, not the area. Similarly, multiplying (2 times Pi) by the radius is more related to the calculation of the circumference of a circle than its area. Lastly, using Pi times height refers to the formula for the volume of a cylinder and does not pertain to circles at all.

Thus, the correct answer, Pi times Radius squared, accurately represents how to calculate the area of a circle.