Sand is falling into a conical pile at the rate of 10 m3/sec such that the height of the pile is always half the diameter of the base of the pile. Find the rate at which the height of the pile is changing when the pile is 5 m. high.

Question

h= r=5
V= (1/3)π(r)(r)(h)
dV/dt=3π(h)(h)(dh/dt)
10=45π(dh/dt)

The answer is supposed to be 2/5π m/s, but i don't see how.

Answer 1

from your
V= (1/3)π(r)(r)(h) , but r = h
V = (1/3)π h^3
dV/dt = π h^2 dh/dt
plug in the values ....

10 = π(25) dh/dt
dh/dt = 10/(25π) = 2/(5π)

I have no idea how you got your derivative.

Answer 2

Sand falls into a Konica on file at the rate of 10 ft^3/minsThe radius of the base of the fire is always equal to 1/2 of its altitude how fast is the altitude of the fighting greasing when it is 5th deep