Question Number 101974 by Ari last updated on 05/Jul/20

Commented byprakash jain last updated on 05/Jul/20

Can you please attach image to this  question. There is an option to  attach image

Answered by Ari last updated on 05/Jul/20

Commented byprakash jain last updated on 06/Jul/20

Fig A  ((πr^2 )/(πR^2 ))=(2/3)⇒(r^2 /R^2 )=(2/3)  Fig C: Assume angle α for shaded area  (((α/2)R^2 )/(πR^2 ))=(3/5)⇒α=((6π)/5)  Fig B (shaded area angle  (((α/2)r^2 )/(πR^2 ))=((((6π)/(10))r^2 )/(πR^2 ))=(6/(10))×(2/3)=(2/5)

Commented byAri last updated on 06/Jul/20

Yes,correct!

Answered by JDamian last updated on 06/Jul/20

From fig. C, for any similar circle, the  colored part is 3/5. So the colored part in  B is 3/5 from the inner circle((3/5)πr^2 ).  From A,    ((πr^2 )/(πR^2 ))=(2/3)    ⇒   πr^2 =(2/3)πR^2   Thus,(((3/5)πr^2 )/(πR^2 ))=(((3/5)∙(2/3)πR^2 )/(πR^2 ))=(3/5)∙(2/3)=(2/5)=40%

Commented byAri last updated on 06/Jul/20

Yes,correct!