1. ## Related Rates

Im having alot of difficulty with this question, I just cannot get the right answer for this one.

A water trough is 8 m long and its cross-section is an isosceles trapezoid which is 210 cm wide at the bottom and 350 cm wide at the top, and the height is 70 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.

V= ?

2. Originally Posted by Steven41
Im having alot of difficulty with this question, I just cannot get the right answer for this one.

A water trough is 8 m long and its cross-section is an isosceles trapezoid which is 210 cm wide at the bottom and 350 cm wide at the top, and the height is 70 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.

V= ?
What if it were full?

(8m)*((210 cm + 350 cm)/2)*(d cm)

This should look familiar, albeit a bit odd for the units.

1) Draw the cross-sectional trapezoid.
2) Construct perpendiculars to the top, through the point of intersection of the base and the sides.
3) Contemplate the triangles on the two ends. You should have created two.
4) The base of these new triangles is (350 - 210) / 2. Do you see why?
5) Notice that as you play with the water level, you get lovely similar trianlges on the two ends.

This should lead you to a solution.