Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality.

Sample Practice Questions (3)

A circle has an arc length of

10 π

units intercepted by a central angle. If the radius of the circle is

20

units, what is the measure of the central angle in radians?

\frac{π}{2}

radians

2 π

radians

\frac{π}{4}

radians

π

radians

An arc of length

14

inches is intercepted by a central angle of

3.5

radians in a circle. What is the radius of the circle, in inches?

0.25

inches

4

inches

10.5

inches

49

inches

A circular pizza has a radius of

8

inches. A slice of pizza is cut with a central angle of

4 5^{\circ}

. What is the area of this slice, to the nearest square inch?

10

square inches

25

square inches

50

square inches

64

square inches

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