the sector of a circle has a central angle θ=(π/4) and area (9π/8) ft2., what is the radius of the circle?

Let r ft be the radius of the circle.

Area of the sector in ft²:
(1/2) × r² × (π/4) = 9π/8
r² = (9π/8) × 2 × (4/π)
r² = 9
r = 3

The radius of the circle = 3 ft

radius = 3 ft

Sector is 1/8 of circle, so area = πr^2/8 = 9π/8
r = 3

Let a be the circle's area.
(pi/4)/2pi = (9pi/8)/a
1/8 = 9pi/(8a)
a = 9pi
Let r be the radius.
9pi = pir^2
r = 3ft

The central angle shows that the sector is 1/8 of a whole circle, so the area of the whole circle would be 9*pi ft^2, so the radius of the circle is 3 feet.

Remember
A = pi r^2
A(sector) =( angle / 2pi) X pi r^2
Hence
(9pi/8) = ((pi/4)/2pi) pi x r^2
9pi/8 = pi/2 x r^2
r^2 = (9pi/8) / (pi/ 2)
r^2 = 9pi/8 X 2/pi

Cancel down by '2' & 'pi'
Hence
r^2 = 9/4
r = sqrt(9/4) = 3/2 = 1 1/2 ft.