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'Gutter' printed from http://nrich.maths.org/
A plastic gutter is designed to catch water at the edge of a roof.
Manufacturers need to minimise the amount of material used to make their product while maximising the volume of water that can be drained.
What is the optimal cross-section for a gutter?
You might want to start by investigating gutters with a rectangular cross-section. Choose a fixed length for the cross section and vary the length of the base of the gutter. How does the area of the cross section change?
Using the same length
, investigate triangular cross-sections. Vary the angle. How does the area of the cross section change?
Finally, use the same length
and investigate cross-sections made from circular arcs. Vary the angle that defines the arc. How does the area of the cross section change?