Question

In a circle, a central angle whose measure is pi/2 radians intercepts an arc whose length is 3pi/2 centimeters. How many centimeters are in the radius of the circle?

Answer 1

3pi/2 cm = quarter of circumference
=> pi*r/2
=> r = 3 cm.

Answer 2

r = 3

pi/2 is to 2 pi as (3 pi / 2) is to (2 pi r)

1/4 = ((3 pi)/2) / 2 pir
12 pi / 2 = 2 pi r
6 pi = 2 pi r
3 = r

Answer 3

\[\theta=\frac{s}{r}\]
where s is the arc length in radians and r is the radius
\[r=\frac{s}{\theta}=\frac{\frac{3\pi}{2}}{\frac{\pi}{2}}=\frac{6\pi}{2\pi}=3\]