A conical tank has a radius of 5 ft and a height of 10 ft. Water runs into the tank at the constant rate of 2 cubic feet per minute. How fast is the water level rising when the water is 6 ft deep?
2007-12-09 05:19:14 · 1 answers · asked by burgler09 5 in Science & Mathematics ➔ Mathematics
What type of conical tank? There are two possibilities: vertex in the top & vertex in the bottom. I am answering the case when vertex is in the bottom.
The volume of the whole tank is V = (1/3) π r² h = 250 π / 3 = 261.8 ft³.
The volume of the water in our tank is V = (π/12) x³, where x is the height of the water level.
The rate of change of the volume as a function of time is dV/dt = (dV/dx) * (dx/dt).
Substituting dV/dx = 2 and dV/dx = (π/6)x² we get dx/dt = (12/π)(1/x²)
For x = 6 feet we get the answer 0.106 ft/min.
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2007-12-09 08:57:48 · answer #1 · answered by oregfiu 7 · 1⤊ 0⤋