In the adjoining figure, AB is the arc of circle with the radius 28 cm and centre O. three concentric circles arcs are drawn in such a way so that OG=GE=EC=CA. Find the area of the shaded region if angle BOA = 30 degree
Answers
Answered by
3
Answer:
PQ and AB are the arcs of two concentric circles of radii 7 cm and 3.5 cm respectively.
Let r
1
and r
2
be the radii of the outer and the inner circle respectively.
Suppose θ be the angle subtended by the arcs at the centre O.
Then r
1
=7 cm, r
2
=3.5 cm and θ=30
o
Area of the shaded region = Area of sector OPQ − Area of sector OAB
=
360
o
θ
πr
1
2
−
360
o
θ
πr
2
2
=
360
o
θ
π(r
1
2
−r
2
2
)
=
360
o
30
o
×
7
22
[7
2
−3.5
2
]
=
12
1
×
7
22
×(49−12.25)
=
12
1
×
7
22
×36.75
=9.625
Therefore, the area of the shaded region is 9.625 cm
2
.
Similar questions