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 Question from Stuart: If a lake were to rise one foot - how many linear feet would it spread onto the shore line ? What is the correlation - 1 foot of a rise = 10 feet onto the shore ? Does it depend on the lake size - if so Lake Ontario in Canada.

Hi Stuart,

Yes it depends on the lake size and length of the shoreline. More importantly it depends on the shape of the shoreline. For example here is an image of the shoreline at Sandbanks Provincial Park.

Image by C. Löser

The beach slopes very gently from the shoreline and a one foot rise in the water level in the lake would result in the shoreline moving a considerable distance up the beach.

In comparison this image of Scarborough Bluffs shows the bluffs very close to the shoreline.

Image by Benson Kua,

A one foot rise in the water level here would result in the shoreline moving very little.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.