A cone-shaped coffee filter of radius 6cm and depth 10cm contains water, which drips out through a hole at the bottom at a constant rate of 1.5cm^3 per second.

a) If the filter starts out full, how long does it take to empty?

v = (1/3)(pi)(r^2)h - 1.5t

0 = (1/3)(pi)(6^2)(10) - 1.5t

0 = 376.99 - 1.5t

376.99 = 1.5t

t = 251.33 sec

b) Find the volume of water in the filter when the depth of the water is h cm.

v = (1/3)(pi)(r^2)h - 1.5t

v + 1.5t = (1/3)(pi)(r^2)h

h = (v + 1.5t) / ((1/3)(pi)r^2)

c) How fast is the water level falling when the depth is 8cm?

8 = (v + 1.5t) / ((1/3)(pi)r^2)

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