Drain Pipes Shape Investigation
Introduction
A builder has a sheet of plastic measuring 2m by 50cm, which he uses
to make drains. The semi-circle is the best shape for a drain.
Prove this.
I will prove this by comparing its volume to that of other shapes.
On older houses there are semi-circular drains but on newer houses
there is fancier ones like pentagon shapes. Is this because they are
better or is it simply for design?
To find the volume of a 3D object I have to find the area of a cross
section and then multiply that by the length of the object. To make it
easier IÂ’m going to change the dimensions of the 2m to 200cm so that
the entire dimensions are the same. We are now working with dimensions
of 200cm and 50cm.
Semi Circle Drain
The first drain we are going to measure is the semi-circular one. So
that we can compare it to the volume of other shapes.
The shape with the biggest cross-section area will have the biggest
volume as IÂ’m going to multiply that by 200 each time.
I have to choose which way IÂ’m going to bend the sheet of plastic.
I will either bend it like fig 1 or like fig2.
[IMAGE]
[IMAGE]
50cm 50cm
200cm 200cm
FIG1 FIG2
surface area by taking a sample of 10 or 20 - this would give a good
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