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# Word Problems/Help

Question
Water runs into a conical tank (pointy part facing downward) at the rate of 12 ft^3/minute. The tank stands down and has a height of 12 ft. and a base radius of 6 ft. How fast is the water level rising when the water is 10 ft deep?

The tank is an inverted cone with height of 12 ft and radius of 6 ft.
The water in the tank is the shape of a cone with height h, radius r, and volume V.
dV/dt = 12 ft³/minute
The water and tank are similar cones, so r = h/2.

V = ⅓πr²h = πh³/12
dV/dh = πh²/4

dV/dt = dV/dh · dh/dt
12 = πh²/4 · dh/dt
dh/dt = 48/(πh²)

When h = 10, dh/dt = 48/π10² ≅ 0.153 ft/minute.
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Word Problems

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#### Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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