question from terry lee volume (1 Viewer)

[mathsbrain]

Was reading volumes by terry lee and it was a trapezoidal solid/frustum and we had to find the volume using similar solids. Mr Lee's answer claimed that the height (h) of the solid is linearly dependent to x which measures the length of the typical slice/cross-section. Is this valid? i mean we can use similar triangles to prove it, but how do we see it by inspection like Mr.lee? And so, under what situation will this "theory" apply?

 

[BenHowe]

If the shape has a rectangular cross section then the area for a particular slice can be given by the product of two lines i.e. A=lw. so you can just as say the width of the base of the shape to be w=mh+c and youll be given measurements to evaluate m,c. Similarly you can do the same for the length i.e. l=mh+c. Note h is just for height. A good example of this is q9 i think for the mcq for mx2 last year. Its a v good method.

 

[mathsbrain]

If the shape has a rectangular cross section then the area for a particular slice can be given by the product of two lines i.e. A=lw. so you can just as say the width of the base of the shape to be w=mh+c and youll be given measurements to evaluate m,c. Similarly you can do the same for the length i.e. l=mh+c. Note h is just for height. A good example of this is q9 i think for the mcq for mx2 last year. Its a v good method.

Hmm...im still not convinced for some reason...i understand the slice's area is given by A=lw, but how do we know w and h is LINEARLY dependent? As in, why can't w=mh^2+c for example?

 

[InteGrand]

Hmm...im still not convinced for some reason...i understand the slice's area is given by A=lw, but how do we know w and h is LINEARLY dependent? As in, why can't w=mh^2+c for example?

If that were the case, the sides of vertical cross-sections taken from the centre of the base would essentially be parabolic arcs.

It's because the sides of vertical cross-sections from the centre of the base are straight lines that the w is linearly related to h.