Answer:Let's use the formula for the area of a sector to find the radius of the sector:
Area of sector = (1/2) * radius^2 * angle in radians
We know the area of the sector is 75pi/16 and the angle in radians is 3pi/8, so we can plug those values in and solve for the radius:
75pi/16 = (1/2) * radius^2 * 3pi/8
Simplifying:
75pi/16 = (3/16) * radius^2 * pi
Multiplying both sides by 16/3pi:
25 = radius^2
Taking the square root of both sides:
radius = ±5
Since a radius can't be negative, we have:
radius = 5
Therefore, the radius of the sector is 5 units.