find find the area of a circle of radius 12 centimetre
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find find the area of a circle of radius 12 centimetre
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Answer:
Given−
AsectorOABhasitsradiusr=OA=OB=12cm
andthecentralangleAOB=60
0
.
Tofindout−
ar.segmentAPB=?
Solution−
InΔABCwehaveOA=OB(radiiofthesamecircle).
∴∠OAB=∠OBA⟹∠OAB+∠OBA=2∠OAB.
Now∠AOB+∠OAB+∠OBA=60
0
+2∠OAB=180
O
(anglesumpropertyoftriangles).
⟹2∠OAB=120
O
⟹∠OAB=∠OBA=60
0
.
∴ΔAOBisanequilateralonewithsidea=12cm.
Soar.ΔAOB=
4
3
a
2
=
4
3
12
2
cm
2
=36
3
cm
2
.
Againar.sector=
360
o
θ
×πr
2
whenθisthecentralangle
&ristheradiusofthesector.
Herer=a=12cmandθ=60
0
.
ar.sectorAOBP=
360
o
60
o
×3.14×12
2
cm
2
=75.36cm
2
.
ar.segmentAPB=ar.sectorAOBP−ar.ΔAOB
=(75.36−36
3
)cm
2
.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Area of circle = [tex]\pi r^{2}[/tex]
22/7 × [tex]12^{2}[/tex]
22/7 × 144
3.14 × 144
452.16 [tex]cm^{2}[/tex]
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