A circle with radius 5 has a sector with a central angle of 9/10 pi radians

First, find out how many degrees 9/10pi radians is. You can multiply it by 180/pi.

9/10pi * 180/pi = 162 degrees

To find the arc sector length, the formula is n/360 * circumference of the circle (pi*r*2) where n is the central angle in degrees and r is the radius.
162/360 * pi*2*5
162/360 * 10 pi/ 1
which is 9/20 pi.

To find arc sector area, the formula is n/360 * area of circle (pi*r^2)
162/360 = pi * 5^2
which is 45pi/4