find the arc length , perimeter angle the angle if the sector area is 336sq.cm and radius is 28cm.
Answers
perimeter of a circle= 2piR.
So perimeter =2×(22÷7)×28=2×22×4=44×4=176cm
To find the arc length:Formula is
(Angle/360)×2piR
We have to find the angle first to find the arc length.
Area of the sector =336sq.cm(Given)
This implies:
(Angle/360)×Pi×R×R=336sq.cm(This is due to the fact that:Area of a sector=Angle/360)×Pi×R×R)
Let the angle be X.
Then:
(X/360)×(22÷7)×28×28=336
Now you have to solve for X.
(X/360)×22×4×28=336
(X/90)×22×28=336
(X/45)×11×28=336
(X/45)×308=336
(X/45)=336÷308
X=(336/308)×45
X=49.0909 or Approximately 50 degrees
Now we can substitute 50 degree in the arc formula.So,
(50÷360)×2PiR=(50÷360)×2×(22÷7)×28=(5÷36)×2×(22÷7)×28
=(5÷36)×2×22×4=(5÷9)×2×22=(5×44)÷9
=220÷9=24.44cm.
Bro just one thing please check the question correctly because in my experience I have never faced an angle with no absolute value.
Therefore the answer to the question is:
Perimeter=176cm
Arc length=24.44cm
Angle subtended=50degree