Question

which expression correctly represents the area a of a circle with a radius r? * 1 point
a = πd
a = (1/2)πr^2
a = (2π)r
a = πr^2

Explanation:

Step1: Recall the formula for the area of a circle

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

Step2: Analyze each option

• Option \( A = \pi d \): Here \( d\) is the diameter (\(d = 2r\)), and \( \pi d\) is the formula for the circumference of a circle (\(C=\pi d\)), not the area.
• Option \( A=(1/2)\pi r^{2}\): This is not the standard formula for the area of a full - circle. The formula \(A=(1/2)\pi r^{2}\) is the area of a semi - circle.
• Option \( A=(2\pi)r\): \(2\pi r\) is the formula for the circumference of a circle (\(C = 2\pi r\)), not the area.
• Option \( A=\pi r^{2}\): This matches the standard formula for the area of a circle.

Answer:

\(A=\pi r^{2}\) (the fourth option)