Rate of increase of a radius and height of a cone

[brandy]

Homework Statement

when powder or granular solids are piled up. the powder forms a conical pile. the edge of the pile reaches a certain maximum angle with the horizontal, called the angle or repose.

A) a pile of coal is found to have an angle of repose of 38%
what is the relationship between height of the pile and its radius.

i got that bit: h=r*Tan a
h= height, r=radius a= Angle of repose

B)if a conveyor belt pours the coal onto the pile at a rate of 0.3m^3/min, at what rate is the radius increasing when the radius is 1.7m

i think i might have to derive the equaiton but i really don't know. i think i need the formula for the area of cone but i don't know. if i did i wouldn't be posting here!

 

[lanedance]

hi brandy

you are given a volumetric rate of change (dV/dt) and want to know the rate of change of the radius (dr/dt).

Can you write the volume of a cone in terms of its radius? You will probably have to use your results form a) to write the height in terms of the radius as well.

Then you can look at differentiating to relate the rates

 

[Chaos2009]

A cone has a third of the volume of a cylinder with the same height and base. Can you find the volume of the cone with that?