In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc
(ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Answers
Answer:
Step-by-step explanation:
In the mentioned figure,
O is the centre of circle,
AB is a chord
AXB is a major arc,
OA=OB= radius =21 cm
Arc AXB subtends an angle 60
o
at O.
i) Length of an arc AXB =
360
60
×2π×r
=
6
1
×2×
7
22
×21
=22cm
ii) Area of sector AOB =
360
60
×π×r
2
=
6
1
×
7
22
×(21)
2
=231cm
2
iii) Area of segment (Area of Shaded region) = Area of sector AOB− Area of △AOB
By trigonometry,
AC=21sin30
OC=21cos30
And, AB=2AC
∴ AB=42sin30=41×
2
1
=21 cm
∴ OC=21cos30=
2
21
3
cm
∴ Area of △ AOB =
2
1
×AB×OC
=
2
1
×21×
2
21
3
=
4
441
3
cm
2
∴ Area of segment (Area of Shaded region) =(231−
4
441
3
) cm
2
Answer:
i) length of Arc =x/360×2πr
ii) area of sector =x/360×πr^2
iii) area of segment=area of sector-area of tringle
where x is angle
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