 # Surface Area of Circle Formula

Circle is nothing but the 2-D representation of a sphere. The total area that is taken inside the boundary of the circle is the surface area of the circle. When we say we want the area of the circle, then we mean surface area of the circle itself.

When the length of the radius or diameter or even the circumference of the circle is already given, then we can use the surface formula to find out the surface area. The surface is represented in square units.

The surface of a circle is given as

$$\begin{array}{l}\large Surface\;Area\;of\;a\;circle: A=\pi \times r^{2}\end{array}$$

### Solved example

Question: What is the radius of the circle whose surface area is 314.159

$$\begin{array}{l}cm^{2}\end{array}$$
?

Solution:

Using the formula:

$$\begin{array}{l}A=\pi \times r^{2}\end{array}$$

Substituting

$$\begin{array}{l}314.159=\pi \times r^{2}\end{array}$$

$$\begin{array}{l}314.159=3.14 \times r^{2}\end{array}$$

$$\begin{array}{l}r^{2}=\frac{314.159}{3.14}\end{array}$$

$$\begin{array}{l}r^{2}=100.05\end{array}$$

$$\begin{array}{l}r=\sqrt{100.05}\end{array}$$

$$\begin{array}{l}r=10\;cm\end{array}$$