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Question Number 62363 by Tawa1 last updated on 20/Jun/19

Answered by MJS last updated on 20/Jun/19

big circle (let R=1)  x=±(√(1−y^2 ))  lines of tbe triangle  x=±((√3)/3)y  looking for an y>0 for which    ((√3)/3)y−(−((√3)/3)y)=(√(1−y^2 ))−((√3)/3)y  (√3)y=(√(1−y^(i2) ))  3y^2 =1−y^2   y=(1/2)  ⇒ r=((√3)/6)  (((3/2)r^2 π)/((1/2)R^2 π))=(1/4) ⇒ 25% are shaded

bigcircle(letR=1)x=±1y2linesoftbetrianglex=±33ylookingforany>0forwhich33y(33y)=1y233y3y=1yi23y2=1y2y=12r=3632r2π12R2π=1425%areshaded

Commented by Tawa1 last updated on 20/Jun/19

God bless you sir

Godblessyousir

Answered by mr W last updated on 20/Jun/19

R=radius of big semicircle  r=radius small semicircles  R^2 =(3r)^2 +((√3)r)^2   ⇒R^2 =12r^2   A_(shade) =3×((πr^2 )/2)=((3πr^2 )/2)  A_(total) =((πR^2 )/2)  ⇒(A_(shade) /A_(total) )=((3r^2 )/R^2 )=((3r^2 )/(12r^2 ))=(1/4)

R=radiusofbigsemicircler=radiussmallsemicirclesR2=(3r)2+(3r)2R2=12r2Ashade=3×πr22=3πr22Atotal=πR22AshadeAtotal=3r2R2=3r212r2=14

Commented by mr W last updated on 20/Jun/19

Commented by Tawa1 last updated on 20/Jun/19

God bless you sir

Godblessyousir

Commented by Tawa1 last updated on 20/Jun/19

God bless you sir

Godblessyousir

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