00:01
In the given question we are told that we have to find the length of the arc of a circle with diameter 14.
00:08
So there is a circle and there is we have to find the length of the arc of a circle with diameter 14 meters which substance where in the circle where a central angle of 5 pi by 6 is subtended.
00:24
So in this circle we are told that there is an angle of 5 pi by 6 subtened.
00:30
Subtended at the center and we have to find the length of this arc right so what we could do over here is to use a proper use a formula that says the length of an arc is can be found by taking theta times r where theta is the central angle theta is the central angle in radiant measure and r is the radius of the circle s is of course the length of the arc right so now what we could do is we can write since the diameter is given to be 14 meters the radius is half of the diameter which is 7 meters so then we can write s is then equal to the angle is already given as 5 pi by 6 so 5 5 5 by 6 times r would be times 7 and this would give us the length of the arc as 35 35 pi by 6 so when we take 35 times pi and divide it with 6 what we get as the value of s is 13 no 18 .3 to 6 so this is in meters right since the radius is in meters we can take the arc length in meters as well so this is the first part of the question now in the second part what we are told to find is the area of a sector in a triangle in a circle let's draw it separately so in this circle we are told that there is a central angle of 30 degrees of 30 degrees and the radius of this circle is 20 centimeter and what we have to find is the area of this sector of this area of this sector which is having a central angle of 30 degrees so what we could do over here is we know that the area of a circle area of a circle can be simply taken as pi r squared right pi r squared and this is 4, a 360 degree sector, right? a 360 degree sector means it is basically a circle, right? so over here, when it is a sector, the area is theta divided by 360 degree times pi a square.
03:20
So now on substituting the value of the central angle in the formula, in the place of theta, we can simply find the area of the sector corresponding to that central angle.
03:34
So, over here it is 30 degrees divided by 360 degrees times pi times 20 squared, which is the radius that is given in the question...