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
`(90^(\circ))/(360^(\circ)) = (1)/(4)` of the whole circle.

This means that the length of the intercepted arc
`\stackrel{\frown}{AB}` is
`(1)/(4)` of the circumference of the circle. So,


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