This problem can be solved if an assumption is made about the angle of repose for a sand pile. According to Wikipedia, the angle of repose for dry sand is ~ 34°. A little bit of trig shows that with this angle, the relationship between the radius of the circular base,r, and the height, h , is r = h tan(56°)
The volume, V, is (1/3) π r2 h. = (1/3) π [h tan(56°) ]2 h
The time derivative of this is equal to the rate at which sand is being added. So
15 = π h2 [tan(56°)]2 dh/dt
Plugging in h =2 and solving for dh/dt yields:
dh/dt = 2.17 m/min.