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Find the area of all shaded regions. Give your answer as a completely simplified exact value in terms of pi. (no approximations)

Find The Area Of All Shaded Regions Give Your Answer As A Completely Simplified Exact Value In Terms Of Pi No Approximations class=

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lc19668

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Answer:

[tex]7\pi cm^{2}[/tex]

Step-by-step explanation:

The shaded area will be the area of the larger circle minus the areas of the two smaller circles. The smaller circles are identical as they have the same radius length.

Therefore, we can create an equation:

⇒ [tex]A = \pi r^{2} - 2\pi r^{2}\\[/tex]

⇒ [tex]A = \pi (3)^{2} - 2\pi (1)^{2}[/tex]   [sub in values]

⇒ [tex]A = 9\pi - 2\pi \\[/tex]   [simplify]

⇒ [tex]A = 7\pi cm^{2}[/tex]   [collect like terms]

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