Question

Sand is poured at the rate of 10 m cube /min so as to form a conical pile whose altitude is always equal to the radius of its base.

Answer 1

dV/dt = 10 m^3/min
V = (1/3) pi r^2 h = (1/3) pi r^3
dV/dr = pi r^2
dV/dr* dr/dt = pi r^2 dr/dt
so
dV/dt = 10 = pi r^2 dr/dt
dr/dt = dh/dt = 10 /pi r^2
or whatever it is you are supposed to solve for

Answer 2

After you finish typing the rest of your problem, take a look at the series of
"Similar Questions" at the bottom of this page. There is a nice variety of them
going back quite a while. One of them should match your problem, all you have to
do is change the numbers.