  # A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of1 ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 9inches deep?X ft/min

Question help_outlineImage TranscriptioncloseA trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 9 inches deep? X ft/min fullscreen
check_circleExpert Solution
Step 1

Let the volume of the water in the trough at time be V. The rate of change of V is,

Step 2

Let h be the depth of water in the trough, which is equal to the height of the triangle which the water makes at the end of the trough.

Step 3

The following equation can be formed which...

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### Calculus 