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?
Answers
Answered by
0
Answer:
Correct option is B)
Let r,ρ,R be the radii of small, medium and big circles respectively.
Radius of small circle =r=4 cm.
Radius of medium circle =ρ=4×
2
3
=6 cm. (small:medium=2:3)
Radius of big circle =R=2×6=12 cm.
(a) Area of unshaded part =2×πr
2
+2×πρ
2
=2π(4
2
+6
2
)=104π cm
2
Area of big circle =πR
2
=12
2
π=144π
Area of shaded part =πR
2
−104π=144π−104π=40π cm
2
(b) Fraction of area shaded =
144π
40π
=
18
5
.
∴ The answer is [B].
Answered by
0
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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