Please point out where I got wrong.
The question:
At a sand gravel plant, sand is falling off a conveyor belt and onto a conical pile at the rate of 10m^3 / min. The diameter of the base of the cone is approximately 3 times the altitude. At what rate is the height of the pile changing when it is 15 meters high?
My solution:
Let V be the volume of the conical pile, and the height be h, and the radius, r.
Given, dv/dt = 10.
Since the diameter of the base is approximately 3 times the altitude, h= 6r, and r = 2.5 m
h=6r
dh/dr = 6
v=1/3 πr^2h
v=1/3 πr^2(6r)
v=2 πr^3
dv/dr = 6πr^2
dv/dt= dr/dt X dv/dr
dr/dt= 10 / 6π(2.5)^2
= approximately 0.0848826 m/min
dh/dt = dr/dt X dh/dr
=0.0848826 X 6
=0.5092956 m/min (my wrong Ans)
But the answer should be 0.0063m/min. Please explain to me where I got wrong.