Question-218886

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Question Number 218886 by Spillover last updated on 17/Apr/25

Answered by mr W last updated on 17/Apr/25

Commented by Spillover last updated on 17/Apr/25

$${perfect} \\ $$

Commented by mr W last updated on 17/Apr/25

2R−2r=18 ⇒R−r=9 R−(√(r^2 −(R−r)^2 ))=10 R−10=(√(2Rr−R^2 )) ⇒R=50 ⇒r=41 A_(shade) =π(R^2 −r^2 )=819π ✓

$$\mathrm{2}{R}−\mathrm{2}{r}=\mathrm{18}\:\Rightarrow{R}−{r}=\mathrm{9} \\ $$$${R}−\sqrt{{r}^{\mathrm{2}} −\left({R}−{r}\right)^{\mathrm{2}} }=\mathrm{10} \\ $$$${R}−\mathrm{10}=\sqrt{\mathrm{2}{Rr}−{R}^{\mathrm{2}} } \\ $$$$\Rightarrow{R}=\mathrm{50}\:\Rightarrow{r}=\mathrm{41} \\ $$$${A}_{{shade}} =\pi\left({R}^{\mathrm{2}} −{r}^{\mathrm{2}} \right)=\mathrm{819}\pi\:\checkmark \\ $$

Answered by Spillover last updated on 17/Apr/25