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Related rates question?

I am a bit of trouble with this one ... A conical tank (with the top down) is 10 feet wide and 12 m depth higher. If water is flowing ito the reservoir at a rate of 10 cubic feet per minute, find the change in water depth when the water is 9 feet deep. Ok, so here is what I have: V = 1 / 3 * pi * R ^ 2 H * dV / dt = 10 ft ^ 3/min dV / dt = 1 / 3 * pi * r * 2RH / r * ^ 2 dt dH / dt But now what??? dr / dt is not given, so I do not know how to solve this: (

you missed two points. R and H are linked by similar triangles and the size of the cone. dV / dt is given. at any point, r = 5 / 12 H V = pi / 3 pi r ^ = 2H / 3 25 / 144 H ^ 3 = 25pi/432 dVdt = H ^ 3 dV / dH dH / dt = H ^ 2 25pi/144 dH dt dV / dt is given by 10 ^ 10 m = 3/min 25pi/144 H ^ 2 dH / dt dH / dt = 288/5pi 1 / H ^ 2 So for H = 9, dH / dt = 32 / (45pi) fpm

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