Can someone help me with this problem? Thank you.

A spherical tank of radius 10ft is being filled with water. When it is completely full, a plug at its bottom is removed. According to Torricelli's law, the water drains in such a way that dV/dt = -k*sqrt(y), where V is the volume of water in the tank andkis a positive empirical constant.

a) Find dy/dt as a function of the depthy

b) Find the depth of water when the water level is fallingat leastrapidly (you will need to compute the derivative of dy/dt with respect to y)

Regarding a), I have done this:

V=1/3*pi*y^2(3a-y) whereais the radius

dV/dt=10*pi*2y(dy/dt) - (1/3)*pi*3y^2(dy/dt)

-k*sqrt(y) = (dy/dt)(20*pi*y - pi*y^2)

dy/dt=-[(k*sqrt(y))/pi*y(20-y)]

And this is what I came up for dy/dt as a function of the depth y

But I am not sure how to proceed with point b) Any help will be apprecited.