Question

A circle has a radius of 7.5 centimeters and a central angle AOB that measures 90 degrees. What is the length of the intercepted arc AB

Answer 1

Since there are $360^{\circ}$ in a circle, and central $\angle AOB = 90^{\circ}$, you can see that the part "sliced out" by the central angle is $\frac{90^{\circ}}{360^{\circ}} = \frac{1}{4}$ of the whole circle.

This means that the length of the intercepted arc $\stackrel{\frown}{AB}$ is $\frac{1}{4}$ of the circumference of the circle. So,

$\stackrel{\frown}{AB} = \frac{1}{4}(2 \pi r) = \frac{1}{4}(2 \pi (7.5 cm)) = \bf \frac{15 \pi}{4} cm$