Question

sand is being pulled by a conveyer belt and dumped at a rate of 50 cubic feet per minute. It forms a mound of sand that shaped like a right circular cone whose base and height are always the equal to on another. How fast is the height of mound growing when it is 25 feet high? (volume of a right circular cone is πr^2h/3

Answer 1

dv/dt=dv/dh * dh/dt

Answer 2

v=f(h)
v'=f'(h)
v'|@25 = f'(25)
dv/dt = f'(25)*dh/dt

Answer 3

thank you, is there somewhere I am supposed to plug in f'(25)? @dan815

Answer 4

if
Dan moves twice as many steps as mark
and mark moves 3 times as many steps as bill
What is Dan's steps wth respect to bills steps

Answer 5

dv/dt =50 ... given and you are solving for dh/dt

Answer 6

Dan's_steps=2*Mark's steps

dDan/dmark = 2

marks's_steps=3*bill's_steps
dmark/dbill=3

if bill moves once then mark will move 3, but if mark moves 3 then dan will move twice as much so 6

if bill moves x steps then, mark moves 3*x and dan moves 2*3*x = 6x steps

therefore
dDan/dbill =6

or

dDan/dbill = dDan/dmark *dMark/dbill

Answer 7

similariry for some change in time, you had some change in height, but for some change in height u have some change in volume
dv/dt=dv/dh*dh/dt

Answer 8

rearrange dh/dt

Answer 9

write the volume as a function of height so u can differentiate and see how volume is changing wrt to height

Answer 10

thank you! @dan815