Question no. 4
Q.4. As shown in the figure diameter of outer circle is 12 cm. Ratio of shaded area of upper semi circle to
that of the shaded area in the lower semicircle.


(A) 1 : 1
(B) 11 : 3
(C) 4 : 3
(D) 8 : 27

Dear student,
Area of upper semi circle=πR22=12×227×6×6=117×6×6=3967 cm2Area of 2 upper unshaded semi circle=2×πr22=πr2=227×3×3=1987 cm2Shaded area of upper semi circle=Area of upper semi circle-Area of 2 upper unshaded semi circle=3967 cm2-1987 cm2=1987 cm2Now, Area of lower semi circle=πR22=12×227×6×6=117×6×6=3967 cm2Area of lower big unshaded semi circle=πr122=12×227×92×92=117×92×92=89128 cm2Area of lower small unshaded semi circle=πr222=12×227×32×32=117×32×32=9928cm2Shaded area of lower semi circle=Area of lower semi circle-Area of lower big unshaded semi circle-Area of lower small unshaded semi circle=3967 cm2-89128 cm2-9928cm2=3967 cm2-79228cm2=1584-79228cm2=79228cm2=1987cm2Ratio of Shaded area of upper semi circle to Shaded area of lower semi circle =19871987=11=1:1thus option A is correct

Regards

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