For example, consider a tree with a trunk radius of 10.5 cm; imagine that the plant produced a layer of wood 0.5 cm thick in the previous year. As a consequence, the tree has 32.2 cm2 of new wood that conducts water from roots to leaves. Assume that each leaf loses water at a rate equal to the conducting capacity of 0.1 cm2 of wood; this plant can conduct enough water through its trunk to support 322 leaves. If the tree produces another 0.5 cm of wood this year, the new ring of wood will have a cross-sectional area of 33.8 cm2 . It is larger than the previous ring of wood and can support conduction to a greater number of leaves—338.
Question:
Imagine a tree that has a radius of 20 cm and that produces a new layer of wood 0.5 cm thick (the outer radius of the new wood is 20.5 cm and the inner radius is 20 cm). What is the cross-sectional area of the new layer of wood (CSA = pr2)? If each leaf needs 0.1 cm2 of wood to supply it with water, how many leaves can the tree have? If the tree produces a new ring of wood next year that is again 0.5 cm thick, how many leaves can the tree have next year (assume that wood conducts water for only 1 year, not 2 years)?
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