In a circle of diameter 42cm ,if an arc subtends an angle of 60 ˚ at the centre where ∏=22/7,then the length of the arc is
(a) 22/7 cm
(b) 11cm
(c) 22 cm
(d) 44 cm
Solution :-
As we know that the circumference of a circle is 2 πr.
Here in this post there is a theorem used. Called arc theorem.
Theorem :- An angle subtended by an arc at the center of a circle is equal to the twice from the angle at any point.
One more theory said that, when a minor arc make an angle theta at the center of a circle, then the length of the arc is equal to,
Length of an arc = θ / 360 × 2πr.
Here θ = 60 degree.
Now,
Length of the arc is = 60 / 360 × 2πr.
Length of the arc = 22.
Hence, option C is right.