Help with 2004 HSC (1 Viewer)

[housemouse]

Im not too good with volumes and 2004 dishes out one of them harder volume questions.

Anyone care to explain in question 5 a(iii) why:

h = ax - x(x-a)
and why r = x +2a

 

[Riviet]

h is given by the y-coordinate of the line minus the y-coordinate of the parabola of the same x-coordinate. Radius is the 2a (forms the cylindrical bit) plus the x-coordinate (forms the slanted bit).

edit: hmm, it's a little hard to explain it without the aid of a diagram

 

[housemouse]

Ok thanks for that.

I understand how you get the height but with the radius = x + 2a, is the x just like any point on the slanted line?

 

[Riviet]

but with the radius = x + 2a, is the x just like any point on the slanted line?

Yes, or you can use the parabola to define the general x-coordinate, either's fine.