Question

A cone-shaped coffee filter is draining at a rate of 20 in^3 /min. The filter has a diameter of 8 inches. the radius of the filter is 2/3 the height. how fast is the coffee level falling when the coffee is 3 inches deep?

Answer 1

v = 1/3 pi r^2 h
r = 2h/3, so
v = pi/3 (4h^2/9) h
= 4pi/27 h^3

dv/dt = 4pi/9 h^2 dh/dt
-20 = 4pi/9 * 9 dh/dt
-5/pi = dh/dt

Answer 2

idk what that is hehe