Question

how do you calculate the area of a circle?
a. ( a=pi r^{2} )
b. ( a = 2pi r )
c. ( a=pi d^{2} )
d. ( a=pi(2 r) )

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Analyze each option

• Option a: \(A=\pi r^{2}\), which is the correct formula for the area of a circle.
• Option b: \(A = 2\pi r\) is the formula for the circumference of a circle, not the area.
• Option c: If \(d\) is the diameter (\(d = 2r\)), then \(A=\pi d^{2}=\pi(2r)^{2}=4\pi r^{2}\), which is incorrect.
• Option d: \(A=\pi(2r)\) is also incorrect as it simplifies to \(2\pi r\) (circumference formula).

Answer:

A. \(A = \pi r^{2}\)