Question

Please help with this

Find the area of the shaded regions.

Answer 1

The area of the shaded region is 7π square centimeters.

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:

`\displaystyle A = \pi r^2`

Therefore, the area of Circle B, the entire circle, is:

`\displaystyle \begin{aligned} A_B &= \pi (3)^2 \\ &= 9\pi \end{aligned}`

The area of Circle O is:

`\displaystyle \begin{aligned} A_O &= \pi (1)^2 \\ &= \pi \end{aligned}`

And likewise, the area of Circle C is:

`\displaystyle \begin{aligned} A_C &= \pi (1)^2 \\ &= \pi \end{aligned}`

The area of the shaded area is the area of the Circle B subtracted by the area of Circles O and C. Hence:

`\displaystyle A_\text{shaded} =A_B - \left(A_ O + A_ C\right)`

Substitute and evaluate:

`\displaystyle \begin{aligned} A_\text{shaded} &= (9\pi ) - (\pi + \pi) \\ &= 9\pi - 2\pi \\\ &= 7\pi \end{aligned}`

The area of the shaded region is 7π square centimeters.