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Setler79 [48]
3 years ago
10

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
Mathematics
1 answer:
Julli [10]3 years ago
6 0
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



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