Related Rates- conical pile of sand

[wind]

Hi, I need help with this question.

Sand forms a conical pile as it falls from a conveyer belt onto the ground. the radius of the base of teh cone is alwasy 8 times the height of the pile. the sand is falling at 0.1m^3/s. how fast is teh height incresing when the pile contains 200m^2 of sand?

so the cone is on its base right?

Want

dh/dt

Have
dv/dt = 0.1 m^3/s

v= pi r^2 h /3
v= pi (8h)^2 h/3
v= pi 8h^3 / 3

...now what?

Thanks

 

[wjm11]

Sand forms a conical pile as it falls from a conveyer belt onto the ground. the radius of the base of teh cone is alwasy 8 times the height of the pile. the sand is falling at 0.1m^3/s. how fast is teh height incresing when the pile contains 200m^2 of sand?

so the cone is on its base right?

Want

dh/dt

Have
dv/dt = 0.1 m^3/s

v= pi r^2 h /3
v= pi (8h)^2 h/3
v= pi 8h^3 / 3

First, you forgot to square the 8.

v= pi 64h^3 / 3

Take the derivative:

dv/dt = 64pih^2 dh/dt

Calculate h for the rqd volume of sand. Is that supposed to be 200 m^3?
Finally, solve for dh/dt.

 

[wind]

thanks