# If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?A water trough is 10 m long and has a cross-section in the...

If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?

A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 60 cm wide at the top, and has height 40 cm.

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The first thing that has to be done is to calculate the volume of the water trough that has a cross section in the shape of an isosceles trapezoid.   To do this, we find the area of the trapezoid and multiply by the length of the trough.

The area of the trapezoid is A = 1/2(b1 + b2)h, which is 1/2(20 + 60)40 which gives us an area of 1600 cm^2.  To find the volume in cm, we then multiply this area by 1000cm (10m x 100cm per meter) to get a volume of 1,600,000 cm^3.

The last part of the question does not seem to make sense.  It should probably ask how long will it take the water in the trough to reach 20 cm. deep.  20 cm represents .2meters so, we calculate the following

0.3 m^3/3min = 0.2m/x

This gives us an answer of 2 minutes.  Therefore, it will take 2 minutes to fill the trough to 20cm deep, which represents filling the trough half full.