Answer:
The correct option is A.
Step-by-step explanation:
Given information: The radius of the circle is 20m and central angle of arc XY is 90 degrees.
The central angle of arc XPY is
[tex]\text{Central angle of arc XPY}=360-90[/tex]
[tex]\text{Central angle of arc XPY}=270[/tex]
Multiply this angle by [tex]\frac{\pi}{180}[/tex], to convert is into radian.
[tex]\text{Central angle of arc XPY}=270\times \frac{\pi}{180}[/tex]
[tex]\text{Central angle of arc XPY}=\frac{3\pi}{2}[/tex]
The formula for arc length is
[tex]l=r\theta[/tex]
Where, r is radius and θ is central angle in radian.
[tex]l=20\times \frac{3\pi}{2}[/tex]
[tex]l=30\pi[/tex]
The length of XPY in terms of pie is 30π m. Therefore the correct option is A.
