Find in degrees the angle subtended at the
centre of a circle of diameter 50 cm by an arc
of length 11 cm.
Answers
Step-by-step explanation:
Given:-
A circle of diameter 50 cm by an arc of length
11 cm.
To find:-
Find the angle subtended at the centre of a circle in degrees?
Solution:-
Given that
Diameter of the circle =(d) = 50 cm
We know that
Radius = Diameter/2
Radius (r) = 50/2 cm
Radius of the circle = 25 cm
Length of the arc (l) = 11 cm
Let the angle subtended by the arc at the centre be X°
We know that
Length of the arc (l) = (X°/360°)×2πr units
On Substituting these values in the above formula then
=> (X°/360°)×2×(22/7)×25 = 11
=> (X°/360°) ×(2×22×25)/7 = 11
=> (X°/360°) × 1100/7 = 11
=>( 1100 X°)/(360°×7) = 11
=> (1100X°)/(2520°) = 11
=> 1100X° = 11×2520°
=> X° = 11×2520°/1100°
=> X° = 2520°/100°
=> X° = 252/10°
=> X° = 126°/5 or 25.2°
The angle = 126°/5 or 25.2°
Answer:-
The angle subtended by the arc at the centre of the given circle = 126°/5 or 25.2°
Check:-
Length of the arc (l) = (X°/360°)×2πr units
=> (126/5×360°)×2×(22/7)×25 cm
on cancelling 5
=> (126°×2×22×5)/(7×360°)
On cancelling 7
=> 18°×2×22×5/360°
On Cancelling 18
=> 2×22×5/20
=> 220/20
=> 22/2
=> 11 cm
Verified the given relations.
Used formulae:-
- Length of the arc (l) = (X°/360°)×2πr units
- l = length of the arc
- r = radius of the circle
- X°= angle subtended by the arc at the centre of circle.
- π=22/7