Calc 2 Finding volume of wedge

[dorangospecie]

Sketch: http://img88.imageshack.us/img88/6479/6219ek4.gif

Find the volume of the wedge in figure (A) in above sketch by integrating the area of vertical cross sections.

This is what I have so far:

b(x) = length of base of triangle at position x
h(x) = height of triangle at position x

For b(x) - use similar triangles
8/6 = (8-x)/b(x)
b(x)=3/4(8-x)

How then we would find the h(x) and solve the actual problem? Can anyone please help me out??

 

[rootX]

Note that height of the plane is also dependent on y
so should be h(x,y).

Find the plane equation. z = ax+by+c and so you know the height.

 

[dorangospecie]

Can you please refer to the sketch and tell me the actual numbers used? I am really trying to figure it out, but I genuinely can't.

 

[Hurkyl]

Note that height of the plane is also dependent on y.

I thought he was defining h(x) to be the height of the triangular cross-section -- not the height of the tetrahedron OABC over a point in the xy plane.

 

[Hurkyl]

Can you please refer to the sketch and tell me the actual numbers used? I am really trying to figure it out, but I genuinely can't.

If we tell you the actual numbers used, then you won't learn how to figure things out, right? How does one normally go about trying to find the value of unknown quantities?


Of course, there's more than one way to solve a problem -- your apprach seems perfectly reasonable. Your formula for b(x) looks correct. I made a sanity check by plugging in two known values (x=0 and x=8) to see if it gives the right answer. (Did you remember to make that check?)

I'm confused as to why you aren't using the exact same method to find h(x).