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Question Number 59000 by Learner last updated on 03/May/19

Answered by MJS last updated on 03/May/19

$$\mathrm{the}\mathrm{centers}\mathrm{of}\mathrm{the}\mathrm{small}\mathrm{circles}\mathrm{form}\mathrm{a}\mathrm{square}$$$$\mathrm{with}\mathrm{side}\mathrm{length}2r\Rightarrow \mathrm{its}\mathrm{diagonal}=2\sqrt{2}r\Rightarrow$$$$\Rightarrow \mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{big}\mathrm{circle}=(1+\sqrt{2})r\Rightarrow$$$$\Rightarrow \mathrm{the}\mathrm{shaded}\mathrm{area}={\left[(1+\sqrt{2})r\right]}^2\pi -4r^2\pi =$$$$=(-1+2\sqrt{2})\pi r^2$$

Commented by Learner last updated on 03/May/19

$$thankyousir$$

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