Calculus Help- A conical salt spreader is spreading salt at a rate...
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Calculus Help- A conical salt spreader is spreading salt at a rate...

[From: ] [author: ] [Date: 12-07-17] [Hit: ]
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A conical salt spreader is spreading salt at a rate of 2 cubic feet per minute. The diameter of the base of the cone is 4 feet and the height of the cone is 5 feet.
How fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? Give your answer in feet per minute.

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dV/dt = -2

V = ⅓ πr²h

relationship between radius and height
r / h = 2 / 5
r = ⅖ h
`````````

V = ⅓ πr²h
V = ⅓ π( ⅖ h)²h
V = 4πh³ / 75
````````````````````

V = 4πh³ / 75

differentiate with respect to time, t
V = 4πh³ / 75
V' = (4πh² / 25) h'
h' = 25V' / (4πh²)
h'(3) = 25(-2) / (4π*3²)
h'(3) = -25 / (18π) ≈ - 0.442 ft/min
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