Answer to Question #99001 in Calculus for Kyla

Question

Plant leaf epidermal cells are thin and flat, and can be approximated as having a cylindrical shape with a radius r and a thickness h
The thickness of these cells h is about the same, but the radius r varies from leaf to leaf.
(a) Find expressions for a plant leaf epidermal cell’s absorption and consumption of a nutrient (as for the spherical cell in Chapter 1). Assume the absorption rate per unit surface area is k1 and the consumption rate per unit volume is k2.

Answer 1

Radius of cylindrical $leaf= r$

$Height= h$

$K_1=absorption$ rate per unit surface area

$K_2=Consumption$ rate per unit volume

$Absorption = K_1×πr^2$

$Consumption = K_2×πr^2h$