The Math Forum: Perimeter Efficiency, Practical Use 3

Splitting A Log

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Example 3: Splitting A Log

If a circular log is split in half, (a) what will be the increase in surface area?

k for the circle is 100%

k for a pair of semicircles is = 61.10%.
The new surface area will be 1.64 x the original surface area.

(b) If the log is split into quarters, what will be the increase in surface area?
Perimeter efficiency, k, for the four quarters is 43.99%. The new surface area will be 2.27 x the original surface area of the log.

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	If a circular log is split in half, (a) what will be the increase in surface area? k for the circle is 100%
k for a pair of semicircles is = 61.10%. The new surface area will be 1.64 x the original surface area.
	(b) If the log is split into quarters, what will be the increase in surface area? Perimeter efficiency, k, for the four quarters is 43.99%. The new surface area will be 2.27 x the original surface area of the log.