Question

1. the area of a circle is ( 36pi , \text{cm}^2 ).

(a) find the radius of the circle.
(b) find the circumference of the circle.

Explanation:

Step1: Find the radius

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(A=36\pi\) \(cm^{2}\), we substitute into the formula:
\(\pi r^{2}=36\pi\)
Divide both sides by \(\pi\): \(r^{2} = 36\)
Take the square root of both sides: \(r=\sqrt{36}=6\) \(cm\)

Step2: Find the circumference

The formula for the circumference of a circle is \(C = 2\pi r\). Substitute \(r = 6\) \(cm\) into the formula:
\(C=2\pi\times6=12\pi\) \(cm\)

Answer:

(a) The radius of the circle is \(6\) \(cm\).
(b) The circumference of the circle is \(12\pi\) \(cm\).