Question

2. A circle has an area of 100 square centimeters. Find its radius.

Answer 1

5.64 centimeters

Explanation

the area of a circle is given by:

$\begin{gathered} A=\pi r^2 \\ \text{where r is the radius} \end{gathered}$

then

Step 1

Let

$\begin{gathered} \text{Area}=A=100(cm^2) \\ \text{radius}=\text{ r} \end{gathered}$

now, replace in the formula and solve for r

$\begin{gathered} A=\pi r^2 \\ 100(cm^2)=\pi r^2 \\ \text{divide both sides by }\pi \\ \frac{100(cm^2)}{\pi}=\frac{\pi r^2}{\pi} \\ \frac{100(cm^2)}{\pi}=r^2 \\ \text{take the square root in both sides} \\ \sqrt[]{\frac{100(cm^2)}{\pi}}\sqrt{=r^2} \\ 5.64\text{ (cm)=r} \end{gathered}$

therefore, the radius is

5.64 centimeters

I hope this helps you