Question

The troough down the center of the ccattle barn is 40 cm wwide at thhe top and 20 cm at the botttom .it is 30 cm deep and 8 m long . It iis filled at a rate of 10 dm3/min. What is the rate of rise of water level .
I tried it and me ans is pretty close but not exact so just wanted if somebidy had any ideas?

Answer 1

look at a cross-section of the front of the trough
which would be a parallelogram.
draw verticals from the base to create two equal right-angles triangles, of height 30 cm and width 10 cm, with a rectangle of 20 by 30 between them.
draw an arbitrary water level, with r cm the value within each of the triangles, (length of water level = 20+2r)
let the water level be h cm
by ratio: r/h = 10/30 ---> r = h/3

V = 800(2 triangles + rectangle)
= 800(2(1/2)rh + 20h)
= 800((1/3)h^2 + 20h)

dV/dt = 800((2/3)h dh/dt + 20dh/dt)
1000 = 800(dh/dt)(2h/3 + 20)
1.25/(2h/3 + 20) = dh/dt
dh/dt = 3.75/(2h+60) ----- I multiplied top and bottom by 3

In most of these cases they would ask for the rate for some specific height given.
Are you sure there was not a height given?
If there was, just plug that in for h in the last part.

Notice I changed everything to cm
8 m = 800 cm and
since 1 dm = 10 cm
(1dm)^3 = (10 cm)^3 = 1000 cm^3

Answer 2

yea i was wondering that too but there isn't any height given so i think i will leave the answer with the height !thanks <3

Answer 3

Reiny the answer is suppose to be 65/(120+4h) . I dunno i m not geting itt

Answer 4

I mean 75 not 65