Math CentralQuandaries & Queries


Question from Crystal, a student:

On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc?

Hi Crystal,

The circumference of a circle of radius $r$ cm is $2 \times \pi \times r$ cm. Thus in your case the circumference of your circle is $24 \times \pi$ cm. The 20 cm arc is hence $\large \frac{20}{24 \pi}$ of the circumference of the circle. Using the symmetry of the circle you can see that the central angle which makes the arc is $\large \frac{20}{24 \pi}$ of the $360^o$ which forms the central arc of the entire circle.


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