Related rates
posted by :) .
Sand is being dropped at the rate of 10 cubic meter per minute onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 meters high?

Related rates 
Reiny
Volume = V = (1/3)π r^2 h
but h = 2r > r = h/2
V = (1/3)π (h^2/4)(h)
= (1/12)π h^3
dV/dt = (1/12)π h^2 dh/dt
10 = 2π (64) dr/dt
dr/dt = 10/(128π) m/min
= 5π/64 m/min
check my arithmetic 
Related rates 
:)
Thank you for answering my question. I just can't understand how it come up to the equation 10=2Π(64)dr/dt. I will be very thankful if you elaborate. :)

Related rates 
Reiny
I can see why you are puzzled, since I have two typo errors.
from V = (1/12) π h^3, I should have had ...
dV/dt = (1/4)π h^2 dh/dt
now subbing in our given...
10 = (1/4)π(64) dh/dt
10 =16π dh/dt
dh/dt =10/(16π) = 5/(8π) m/min
I apologize for those blatant errors. 
Related rates 
:)
I'm very thankful for being kind to me. Last one thing, 8 meters is the height of the conical pile. Does it also mean that it is the same as the height of the sand?

Related rates 
Reiny
Since we assume that the pile of sand forms a cone,
the height of the cone is equal to height of the sand pile 
Related rates 
:)
thank you so much. :) you really help me a lot. Godbless!

Related rates 
z
hii... am in the solution with the V = (1/3)π (h^2/4)(h) still have h in 2/4??
isn't the derivative of r = h/2 is just 2/4??
Respond to this Question
Similar Questions

calculus
please help if you can At a sand & gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what … 
calculus
At a quarry, sand is filling off a conveyor onto a conical pile at a rate of 15 cubic feet per minute. The diameter of the base of the cone is four times the height. At what rate is the height of the pile changing when the pile is … 
Timerate problem(calculus)
Sand is being dropped at the rate 10 metercube/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high? 
Calculus  Rate of Change
Can someone explain how to solve this problem? 
Related Rates
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. … 
calculus
Sand is falling into a conical pile so that the radius of the base of the pile is always equal to one half its altitude. If the sand is falling at the rate of 10 cubic feet per minute, how fast is the altitude of the pile increasing … 
Calculus
Sand falls from a conveyor belt onto a conical pile at a rate of 6ft/mi^3. The radius of the base is always equal to twothirds of the pile’s height. At what rate is the height of the pile changing when the radius of the base of … 
Related Rates
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing … 
Calculus
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of … 
Time rates
sand is being dragged at the rate of 10m^3/min into a conical pile. if the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 2m high?