In the figure below,1/3 of circle A is shaded and 3/7 of circle B is shaded. The ratio of the total area of circles A and B to the area of the circle C is 5:8. What fraction of circle C is not shaded?
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Answer:
Area of shaded region = Area of larger semicircle − Area of circle
−2 (Area of small semi-circle)
+Area of small semi-circle
=
2
π
(4.5)
2
−π(
2
4.5
)
2
- area of small semi-circle
=
2
π
(4.5)
2
−π(
2
4.5
)
2
−
2
π
(
2
3
)
2
=π[
2
(4.5)
2
−(
2
4.5
)
2
−
2
1
(
2
3
)
2
]
=π×3.9375=12.375cm
2
Cost of painting = Rs. (12.375×0.25)≈Rs.3
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