## geerky42 3 years ago 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?

1. geerky42

@hartnn @Hero @helder_edwin @jiteshmeghwal9

2. jiteshmeghwal9

sorry @geerky42 no idea :( i'm not good in geometry

3. geerky42

Any idea? @rajathsbhat

4. rajathsbhat

Yes, actually. But tell me, is the trough like this:|dw:1352120844035:dw|?

5. rajathsbhat

i don't get the "12 feet long" part.

6. phi

Is isolates triangles supposed to be isosceles triangles?

7. geerky42

|dw:1352121448125:dw|

8. geerky42

I think this is what question means, but i honestly have no idea...

9. rajathsbhat

where are the triangles? :\

10. geerky42

|dw:1352121575320:dw|

11. geerky42

triangle prism, idk.

12. rajathsbhat

yes! phi's got it right!

13. geerky42

So it's like trapezoid prism or what?

14. geerky42

@mahmit2012 @mayankdevnani

15. rajathsbhat

I think it's a triangular prism.

16. geerky42

An isosceles triangular prism?

17. geerky42

where it has base of 3ft and heigh of 3 ft?

18. phi

the only thing that makes sense is |dw:1352123776310:dw|

19. phi

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

20. phi

$v= 6 h^2$ $\frac{dv}{dt}= 12 h \frac{dh}{dt}$ plug in for h and dh/dt to find dv/dt

21. geerky42

I see, thanks!

22. phi

I still don't know what Its end are isolates triangles means....