Related Rates: Equilateral Triangle Trough

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skiesofgrey

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Nov 11, 2020
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An animal trough with a length of 10 meters and equilateral triangle-shaped ends of height 7 meters is being filled with slop. The slop is pumped in at a rate of 5 m3/min. Find the rate of change of the area of the top surface of the slop when the slop is 3 meters deep in the trough.

What I know:
I managed to solve for the sides of the equilateral triangle-shaped ends of both the trough and slop, which are (14/3)√(3) and 2√(3) respectively. I'm not really sure where to go from there though. I would really appreciate some guidance.
 
skiesofgrey said:
An animal trough with a length of 10 meters and equilateral triangle-shaped ends of height 7 meters is being filled with slop. The slop is pumped in at a rate of 5 m3/min. Find the rate of change of the area of the top surface of the slop when the slop is 3 meters deep in the trough.

What I know:
I managed to solve for the sides of the equilateral triangle-shaped ends of both the trough and slop, which are (14/3)√(3) and 2√(3) respectively. I'm not really sure where to go from there though. I would really appreciate some guidance.
Click to expand...
Can you draw a cross-section of the trough (perpendicular to the length)?
 
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