Posted by Rachel | Posted in Coffee and Accessories | Posted on 10-08-2010
Tags: 2 coffee cone filters, amsti;, coffee, supplies
Related Rates Problem?
A coffee filter has the shape of an inverted cone. Water drains out of the filter at a rate of 10 cm^3/min. When the depth of water in the cone is 8 cm, the depth is decreasing at 2 cm/min. What is the ratio of the height of the cone to its radius?
Please help me out. I have been trying to solve it, but I have no clue how to get the answer.
Thanks.
Let the ratio be a. We know h = ar.
V = pi r^2 h / 3
= pi r^2 (ar)/3
= pi a r^3 / 3
dV/dt = pi a r^2 dr/dt
When h = 8, r = 8/a, so we have (note that dr/dt = d(h/a)/dt = (1/a)dh/dt
dV/dt = pi a (8/a)^2 (1/a)*(-2) = -10
= -128pi/a^2
a = sqrt(128pi/10)
Lily – single cup coffee maker – johnkwarner
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