Question

The figure below shows a circle with a radius of 7 units from which a circle with a radius 3 units has been cut. What is the exact area of the blue region.

Answer 1

To find the blue area, you have to subtract the area of the small circle from the area of the big circle

The rule of the area of the circle is

$A=\pi(r)^2$

r is the radius of the circle

Then the area of blue is

$A_{blue}=A_{big}-A_{small}$

Since the radius of the small circle is 3 units and the radius of the big circle is 7 units, then

$\begin{gathered} A_{blue}=\pi(7)^2-\pi(3)^2 \\ A_{blue}=49\pi-9\pi \\ A_{blue}=40\pi \end{gathered}$

The exact area of the blue part is a 40pi square unit