suppose you are drinking root beer from a conical cup. the cup has a diameter of 8 cm and a depth of 10 cm. as you suck the straw, root beer leaves the cup at the rate of 7 cm^3/second. at what rate is the level of the liquid in the cup changng when the liquid is 6 cm deep?

Answer 1

rate of change of volume = surface area * rate of change of depth
(look at thin slice of area pi r^2 and depth delta h)

what is r?
4/10 = r/6 similar triangles
r = 12/5
surface area = pi(144/25)
so
-7 cm^3/s = pi(144/25) cm^2 * dh/dt
so
dh/dt = -(25*7)/(144 pi) cm/s