Completing the square
4y2+8y=11

4y2+8y=11

(2y+2)^2 -4 = 11

(2y+2)^2 = 15

(2y+2) = +-√15

y= √15 /2 - 1 , -√15/2 -1

y= (√15-2)/2, (-√15-2)/2

i think the amount would be $140.62

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).