Answer:
The area of the shaded region is 7π square centimeters.
Step-by-step explanation:
Note that Circle B has a radius of 3 cm, and the two smaller circles, Circles O and C, both have a radius of 1 cm.
The area of a circle is given by:
[tex]\displaystyle A = \pi r^2[/tex]
Therefore, the area of Circle B, the entire circle, is:
[tex]\displaystyle \begin{aligned} A_B &= \pi (3)^2 \\ &= 9\pi \end{aligned}[/tex]
The area of Circle O is:
[tex]\displaystyle \begin{aligned} A_O &= \pi (1)^2 \\ &= \pi \end{aligned}[/tex]
And likewise, the area of Circle C is:
[tex]\displaystyle \begin{aligned} A_C &= \pi (1)^2 \\ &= \pi \end{aligned}[/tex]
The area of the shaded area is the area of the Circle B subtracted by the area of Circles O and C. Hence:
[tex]\displaystyle A_\text{shaded} =A_B - \left(A_ O + A_ C\right)[/tex]
Substitute and evaluate:
[tex]\displaystyle \begin{aligned} A_\text{shaded} &= (9\pi ) - (\pi + \pi) \\ &= 9\pi - 2\pi \\\ &= 7\pi \end{aligned}[/tex]
The area of the shaded region is 7π square centimeters.
