Word Problems/Help


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 ft/minute
The water and tank are similar cones, so r = h/2.

V = ⅓πrh = πh/12
dV/dh = πh/4

dV/dt = dV/dh dh/dt
12 = πh/4 dh/dt
dh/dt = 48/(πh)

When h = 10, dh/dt = 48/π10 ≅ 0.153 ft/minute.

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Janet Yang


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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