If in a circle of radius r arc length of l subtend θ radian angle at centre then

Math Formulas

If in a circle of radius r arc length of l subtend θ radian angle at centre then

If in a circle of radius r arc length of l subtend θ radian angle at centre then

Example 1 :-The minute hand of a watch is 1.5 cm long. How far does its move in 40 minutes? (Use π = 3.14).

Solution :-
In 60 minutes, the minute hand of a watch completes one revolution. Therefore, in 40 minutes, the minute hand turns through 2/3 of a revolution. Therefore,If in a circle of radius r arc length of l subtend θ radian angle at centre thenradian. Hence, the required distance travelled is given by If in a circle of radius r arc length of l subtend θ radian angle at centre then

Example 2 :-If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.

Solution :-
Let r1 and r2 be the radii of the two circles. Given that If in a circle of radius r arc length of l subtend θ radian angle at centre then Let l be the length of each of the arc. Then If in a circle of radius r arc length of l subtend θ radian angle at centre then which gives If in a circle of radius r arc length of l subtend θ radian angle at centre then

r1 : r2 = 22 : 13.

Talk to Our counsellor