Draw a diagram. When the water has depth y, its surface has width 40+(y/60)(100-40) = y+40
So, the volume of water when depth is y is
v = y(40 + y+40)/2 * 7 = 280y + 7/2 y^2
so,
dv/dt = 280 + 7y dy/dt
Now just plug in your numbers
Yeah, I know the units for v are in m-cm^2, but the factor of 100 is just a linear scale. You can include it if you want.
A water trough is 7 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. 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 40 cm deep?
1 answer
1 answer