Finding the volume of a gutter...

[PhlamngToad]

hey guys, first post, hoping you can help :-D

i've got this gutter problem, there are 3 pieces of metal, 100cm long and 5 cm wide. they make a trapezoid shape with the sides angled 30 degs. away.

so.. the sides are approx. 4.3cm tall, the total volume is 1875*sqrt(3)

i need to find an integral to figure out the volume of water for a water height of h. do i go from 0 to 4.3, put the 100 out in front? i'm not sure where to go from there, it would have to 5+x where x is the added area as the sides spread apart but i'm not sure how to do this, any help is greatly appreciated!

 

[wjm11]

100cm long and 5 cm wide. they make a trapezoid shape with the sides angled 30 degs. away.

so.. the sides are approx. 4.3cm tall, the total volume is 1875*sqrt(3)

PhlamngToad,

I'm a bit confused by your problem statement. If I understand your description, you have a lower trapezoid base of 5 cm and an upper base of (5 + 2h/sqrt3) cm. Therefore, area as a function of height is

A = ((5 + 5 + 2h/sqrt3)/2)*h = 5h + (h^2)/sqrt3

For a height of 4.3 cm, this yields an area of about 32.175 cm^2 (about what you have listed).

Your area times length will give you volume. What more do you need?

 

[PhlamngToad]

i need the volume with respect to H, H is the height of the water.

 

[Gene]

He's right. Volume is 100*area.
V=100*(5h + (h^2)/sqrt(3))
Try h=4.3 to prove it.
--------------------
Gene

 

[PhlamngToad]

ohhh, duh. i don't know why but i wrote down problem, solved it using your help above, and then posted that , i guess after following the work my brian died.

thanks a lot, and thanks gene for making me realize i hadn't thanked him in the first place .