Math CentralQuandaries & Queries


Question from Kyle, a student:

A semi-circular roof guttering contains some water.

The cross-section of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm.
What is the depth of water in the gutter?

Hi Kyle,

I drew the gutter and labeled some points.


C is the center of the circle so CB is a radius and hence its length is 5 centimetres. A is the center of the circular surface of the water and hence CA is perpendicular to AB and the length of AB is 4 centimetres.What does Pythagoras theorem tell you about the length of CA? What is the depth of the water in the gutter?


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