Ms. Davis loves a good cup of coffee. If she puts on a pot of coffee using coneshaped coffee filter of radius 6 cm and depth 10 cm, and the water begins to drip out through the hole at the bottom at a constant rate of 1.5 cm^3 per second, determine how fast the water level is falling when the depth is 8 cm.
Help? :/

Question

myininaya · Answer

volume=V
depth=d
r=radius
we want to find d' when d=8cm
V=1/3  *pi*r^2*d
find derivative we have
V'=1/3*pi*2rr'*d+1/3*pi*r^2*d'
..

anonymous · Answer

Can you show me how you find the derivative?

myininaya · Answer

you use the product rule 
we have two triangles so there is a way we can write this with just d' or d without r or r'

myininaya · Answer

we have to triangles inside the cone so we have 6/r=10/d so r=6d/10=3d/5 so r'=3d'/5

myininaya · Answer

so we have V'=1/3*pi*2*3d/5*3d'/5*d+1/3*pi*9r^2/5*d' so we can find d' plug in the values for V' and d and then solve for d'

anonymous · Answer

so I just plug in 8 to V' ?

myininaya · Answer

i gave us the rate of the volume which was _____________

myininaya · Answer

mean it gave you*

anonymous · Answer

1.5cm^3

myininaya · Answer

yes and the volume is decreasing so it would be negative 1.5cm^3/sec

myininaya · Answer

they wanted us to find d' when d=8cm

myininaya · Answer

so we have everything we need to solve for d'

anonymous · Answer

SO what do I do next?