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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?