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Question Number 135658 by I want to learn more last updated on 14/Mar/21

Answered by mr W last updated on 15/Mar/21

Commented by mr W last updated on 15/Mar/21

shaded area=big circle − small circle =πR^2 −πr^2 =π(R^2 −r^2 ) r^2 +(((16)/2))^2 =R^2 ⇒R^2 −r^2 =(((16)/2))^2 = ⇒shaded area=π(((16)/2))^2 =64π units

$${shaded}\:{area}={big}\:{circle}\:−\:{small}\:{circle} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\pi{R}^{\mathrm{2}} −\pi{r}^{\mathrm{2}} =\pi\left({R}^{\mathrm{2}} −{r}^{\mathrm{2}} \right) \\ $$$${r}^{\mathrm{2}} +\left(\frac{\mathrm{16}}{\mathrm{2}}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$$\Rightarrow{R}^{\mathrm{2}} −{r}^{\mathrm{2}} =\left(\frac{\mathrm{16}}{\mathrm{2}}\right)^{\mathrm{2}} = \\ $$$$\Rightarrow{shaded}\:{area}=\pi\left(\frac{\mathrm{16}}{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{64}\pi\:{units} \\ $$

Commented by I want to learn more last updated on 15/Mar/21

God bless you sir, i appreciate.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\mathrm{i}\:\mathrm{appreciate}. \\ $$

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