Ari B.

asked • 02/10/22

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.

(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.1 feet deep?



(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.2, determine the rate at which water is being pumped into the trough.

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Heriberto E. answered • 02/10/22

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Heriberto E.

a) The rate at which the water level rises, as described by h when the h (or the water level) is 1.1 feet, is (5/33) ft/min. See video and notation for further detail. b) The rate at which water is being pumped into the triangular prism trough, as described by V-- the volume of the pumped water when the water level, or h, is 2.2 feet and rising at a rate of (3/8) in/min or (1/32) ft/min, is (33/40) cubic feet/min.
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02/10/22

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