Question 10·Easy·Circles
In a circle with center , the central angle measures . The circle has a circumference of 30.
What is the length of minor arc ?
For circle arc length questions in degrees, avoid finding the radius unless you must. Instead, treat the central angle as a fraction of 360° (for example, ), then multiply that fraction by the total circumference given in the problem. Do the fraction simplification and final multiplication carefully to avoid small arithmetic mistakes.
Hints
Connect angle measure and arc length
A central angle "uses up" a portion of the circle. How can you express the 60° angle as a fraction of the whole 360° circle?
Use the circumference
Once you know what fraction of the full circle the 60° represents, apply that same fraction to the total circumference, which is 30.
Do the final multiplication carefully
Multiply the fraction you found by 30. Double-check your multiplication and any simplification of the fraction.
Desmos Guide
Compute the fraction of the circle and arc length
In Desmos, type (60/360)*30 or equivalently 30*(60/360) into the expression line. The output is the length of the minor arc ; read that value directly from Desmos.
Step-by-step Explanation
Relate the central angle to the circle
A full circle has . The central angle is part of that full circle.
So the fraction of the circle that this angle represents is:
Simplify the fraction of the circle
Simplify :
So the arc corresponds to of the entire circle.
Use the circumference to find the arc length
The total circumference of the circle is 30, and the minor arc is of the circle.
So the length of arc is:
Therefore, the length of minor arc is 5.