Question

An arc 13. 0 cm in length on the circumference of a circle subtends an angle of 113°. What is the radius of the circle?

1. hongcuc2
If the length of the arc is 13 cm and the angle subtends be 113° then the length of radius is equal to 6.59 cm.
Given that the length of the arc is 13 cm and the angle subtends be 113°.
We are required to find the length of radius of the circle in which the length of the arc be 13 cm and the angle subtends be 113°.
Radius is basically a line which joins a point on the circle to the center point of the circle.
Arc is basically a part of circumference of the circle.
The relationship between length of arc ,angle and length of radius is as under:
s=rΘ , in which s is the length of arc, r is the length of radius and Θ is the angle.
So,we have to first convert 113 degrees into radians.
Using all the values in the relationship:
13=(r*113*π)/180
r=(13*180)/(113*3.14)
r=2340/354.82
r=6.59 cm
Hence if the length of the arc is 13 cm and the angle subtends be 113° then the length of radius is equal to 6.59 cm.