Question

1. what is the circumference of a circle that has an area of 36 m²?

Explanation:

Step1: Find the radius from the area formula

The area formula of a circle is \(A = \pi r^{2}\). Given \(A = 36\space m^{2}\), we have \(36=\pi r^{2}\). Then \(r^{2}=\frac{36}{\pi}\), and \(r=\sqrt{\frac{36}{\pi}}=\frac{6}{\sqrt{\pi}}\) (taking the positive value since radius is non - negative).

Step2: Calculate the circumference using the radius

The circumference formula of a circle is \(C = 2\pi r\). Substitute \(r = \frac{6}{\sqrt{\pi}}\) into the formula: \(C=2\pi\times\frac{6}{\sqrt{\pi}}\). Simplify \(C = 12\sqrt{\pi}\space m\approx12\times1.772 = 21.26\space m\)

Answer:

The circumference of the circle is \(12\sqrt{\pi}\space m\approx21.26\space m\)