A trough filled w/ water's 2m long & has a cross section in the form of an isosceles trapezoid 30 cm wide at the bottom, 60 cm at the top & a height of 50 cm. If the trough leaks water at the rate of 2000 cm^3 / min, how fast is the water level falling when the water is 20 cm. deep.?

Question

A trough filled w/ water's 2m long & has a cross section in the form of  an isosceles trapezoid 30 cm wide at the bottom, 60 cm at the top & a height of 50 cm. If the trough leaks water at the rate of 2000 cm^3 / min, how fast is the  water level falling when the water is 20 cm. deep.?

anonymous · Answer

i don't know what is 2000 cm^3 / min there...

unklerhaukus · Answer

have you found the volume of the trapezoidal-prism?

anonymous · Answer

wait...why i need to find the volume?

unklerhaukus · Answer

because 200 cm^3 /min is the change in the volume (of fluid)

anonymous · Answer

when there is the word rate it means change?

anonymous · Answer

@UnkleRhaukus

unklerhaukus · Answer

yes the rate of flow is the change in the volume with time,

$$\frac{\text dV}{\text dt}$$

anonymous · Answer

the formula of its volume is 
$$V=(1/2)(h)(b _{1}+b _{2})(H)$$
now i know that:
  $$V'$$ is equal to 2000 cm^3/min,
h' is20 cm
how can i begin?

anonymous · Answer

is h' 20 cm? correct me if i'm wrong...?

unklerhaukus · Answer

H=L =2m    right?

anonymous · Answer

yes

anonymous · Answer

what is b sub 1 &2?

anonymous · Answer

30 and 60?

anonymous · Answer

i really don't understand...

unklerhaukus · Answer

|dw:1344512026902:dw|