A cow-trough has a triangular cross-section of height 25cm and base 30cm and is 2m long. A cow is drinking steadily, and when the water level is 5cm below the top it is being loward at the rate of 1cm/min. Find the rate if consumption in litres per minute.

Question

A cow-trough has a triangular  cross-section of height 25cm  and base 30cm and is 2m long. A cow is drinking steadily, and when the water level is 5cm below the top it is being loward at the rate of 1cm/min. Find the rate if consumption in litres per minute.

Steve · Answer

The width of the water surface when it has depth y is 6/5 y. So, the cross-sectional area is (1/2)(y)(6/5 y) = 3/5 y^2

Thus, the volume at depth y is 120y^2 cm^3

We have

dv/dt = 240y dy/dt
Now plug in the numbers and we have

dv/dt = 240(20)(-1) = -4800 cm^3/min

Or, 4.8 L/min

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