Question

If the diameter of a circle is $20\mathrm{cm}$, what is the area?

Answer 1

Step 1: Calculate the circle's area.

Consider the following formula to calculate the area of a circle.

$A={\mathrm{\pi r}}^2$

Where, $A$ represents the area of the circle, $\pi$ are the irrational numbers that contain a constant value as $3.14159...$, and $r$ represents the square of the radius of the circle.

Step 2: Find the value of radius.

The radius is half of the diameter:
$\begin{array}{rcl}r& =& \frac{d}{2}(\therefore d=20)\\ & \Rightarrow & r=\frac{20}{2}\\ & \Rightarrow & r=10\\ \therefore r^2& =& 100\end{array}$
Substitute the values in the formula $A={\mathrm{\pi r}}^2$:

$\begin{array}{rcl}A& =& 100\mathrm{\pi }\\ & =& 314.16{\mathrm{cm}}^2\end{array}$

Hence, the area of circle is $\mathbf{314}\mathbf{.}\mathbf{16}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}$.