Question

the area of a circle is 12.56 square centimeters. what is the circles radius?
round your answer to the nearest hundredth.

Explanation:

Step1: Recall the area formula of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(A\) is the area and \(r\) is the radius. Given \(A = 12.56\space cm^{2}\) and taking \(\pi\approx3.14\).

Step2: Solve for \(r^{2}\)

Substitute the values into the formula: \(12.56 = 3.14r^{2}\). Then, \(r^{2}=\frac{12.56}{3.14}\).

$$r^{2}=4$$

Step3: Solve for \(r\)

Take the square - root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r=\sqrt{4}\).

Answer:

\(2.00\space cm\)