Question

the radius of a circle is 7 yards what is the measure in radians of the angle subtended by an arc 7pi yards long

Answer 1

step 1

Find the circumference of the circle

`C=2\cdot\pi\cdot r`

we have

r=7 yd

substitute

`\begin{gathered} C=2\cdot\pi\cdot7 \\ C=14\pi\text{ yd} \end{gathered}`

step 2

Remember that the length of the circumference subtends a central angle of 2pi radians

so

Applying proportion

Find out the measure of the central angle for an arc of 7pi yards long

`(2\pi)/(14\pi)=(x)/(7\pi)`

solve for x

x=pi radians