Trough - Related Rates Problem

[BlackSheep987]

Okay so I have this related rates problem for my AP Calculus Class
A trough (Extruded Trapezoid) with a height of 2, Base 1 (bottom) of 2, Base 2 (top) of 6 and a extrusion of 10.
(I provided a picture for better understanding)
--------------------------------------…
A = Area of the top surface of the Water
h = Depth of water
V = Volume of Water
The trough empties at a rate of 5 ft^3/min
--------------------------------------…
I have to find dA/dt and dV/dt when h = 1/2 ft

Our teacher gave us the A and V equations in terms of h
A = 10(2+2h)
V = 20 + 10h^2

I need help understanding how he got to the formulas above from the regular Area and Volume Equations
I also need help getting the correct answer when h = 1/2 ft ( I don't know where to get a value for dh/dt)

Here is a link to the picture
http://i.imgur.com/YjXzJ.png

Thanks

 

[LCKurtz]

Okay so I have this related rates problem for my AP Calculus Class
A trough (Extruded Trapezoid) with a height of 2, Base 1 (bottom) of 2, Base 2 (top) of 6 and a extrusion of 10.
(I provided a picture for better understanding)
--------------------------------------…
A = Area of the top surface of the Water
h = Depth of water
V = Volume of Water
The trough empties at a rate of 5 ft^3/min
--------------------------------------…
I have to find dA/dt and dV/dt when h = 1/2 ft

Our teacher gave us the A and V equations in terms of h
A = 10(2+2h)
V = 20 + 10h^2

I need help understanding how he got to the formulas above from the regular Area and Volume Equations
I also need help getting the correct answer when h = 1/2 ft ( I don't know where to get a value for dh/dt)

Here is a link to the picture
http://i.imgur.com/YjXzJ.png

Thanks

Look at the end of the trough and suppose the water has depth h. Do you see from the geometry that the length of the waterline is 2 + 2h?

Then by the formula for the area of a trapezoid, the wetted area of the end is ?
Then the volume of the water is 10 times that value.

That should give you the volume of the water as a function of h. You can check you have it right to see if you get his formula whan h = 2. You differentiate your V,h equation with respect to t to get a relation between dV/dt and dh/dt.

Similarly, but easier, for the surface area.