Circles: Area

Example 1:

What is the area of a circular table with diameter $6$ ft?

Given that, the diameter of the circular table is $6$ ft.

So, the radius of the circular table is half of the diameter. That is, radius is $3$ ft.

Use the formula for area of a circle, $A=\pi r^2$ , where $r$ is the radius of the circle.

Substitute $3$ for $r$ in the formula.

$\begin{array}{l}A=\pi {\left(3\right)}^2\\ =\pi \left(9\right)\\ \approx 28.26\end{array}$

Therefore, the area of the circular table is about $28.26{\text{ ft}}^2$

Example 2:

What is the area of the shaded region in the figure shown?

It's clearly marked that the larger circle has a radius $11$ cm. So, its area is

$\begin{array}{l}{A}_{\text{large circle}}=\pi r^2\\ =\pi {\left(11\right)}^2\\ =121\pi \\ \approx 379.94{\text{ cm}}^2\end{array}$

What about the smaller circle? Well, the distance from the center to edge is $11$ cm; the diameter of the smaller circle is $11-4=7$ cm. So, the radius of the smaller circle is $3.5$ cm.

$\begin{array}{l}{A}_{\text{small circle}}=\pi r^2\\ =\pi {\left(3.5\right)}^2\\ =12.25\pi \\ \approx 39.47{\text{ cm}}^2\end{array}$

To get the area of the shaded region, subtract the area of the smaller circle from the area of the larger circle.

$379.94-38.47=341.47$

Therefore, the area of the shaded region is about $341.47{\text{ cm}}^2$ .