Water is flowing into a hemispherical bowl having a radius of 10cm at constant rate of 3cm^3/min. When the water is x cm deep, The water level rises at a rate of 0.0149 cm/min. What is the value of x?

Answer 1

The first thing is to develpe a relation between depth and volume
In the SPHERICAL CAP (which you can google),

Volume = (pi/3)x2(3R - x)
R=10cm
dV/dt=(PI/3)(6Rx-3x^2) dx/dt
you know dv/dt, and dx/dt. Solve for x. Looks like something of a quadratic equation, use the quadratic formula.