geerky42
A trough is 12 feet long and 3 feet across the top. Its end are isolates triangles with altitudes of 3 feet. If water is being pumped into the trough at 2 cubic feet per min, how fast is the water level rising when the water is 1 foot deep?
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geerky42
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@hartnn @Hero @helder_edwin @jiteshmeghwal9
jiteshmeghwal9
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sorry @geerky42 no idea :(
i'm not good in geometry
geerky42
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Any idea? @rajathsbhat
rajathsbhat
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Yes, actually.
But tell me, is the trough like this:|dw:1352120844035:dw|?
rajathsbhat
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i don't get the "12 feet long" part.
phi
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Is isolates triangles supposed to be isosceles triangles?
geerky42
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|dw:1352121448125:dw|
geerky42
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I think this is what question means, but i honestly have no idea...
rajathsbhat
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where are the triangles? :\
geerky42
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|dw:1352121575320:dw|
geerky42
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triangle prism, idk.
rajathsbhat
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yes! phi's got it right!
geerky42
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So it's like trapezoid prism or what?
geerky42
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@mahmit2012 @mayankdevnani
rajathsbhat
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I think it's a triangular prism.
geerky42
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An isosceles triangular prism?
geerky42
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where it has base of 3ft and heigh of 3 ft?
phi
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the only thing that makes sense is
|dw:1352123776310:dw|
phi
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The ratio of base to altitude of the triangular base is 3/3 = 1
when the water is at height h, the base (width of the water) is also h
|dw:1352123882327:dw|
the area as a function of h is 1/2 h^2
volume is 12 * 1/2 *h^2
phi
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\[ v= 6 h^2\]
\[\frac{dv}{dt}= 12 h \frac{dh}{dt} \]
plug in for h and dh/dt to find dv/dt
geerky42
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I see, thanks!
phi
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I still don't know what
Its end are isolates triangles
means....