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Body surface area One of several empirical formulas that
Chapter 11, Problem 56E(choose chapter or problem)
Body surface area One of several empirical formulas that relates the surface area of a human body to the height h and weight w of the body is the Mosteller formula \(S(h, w)=\frac{1}{60} \sqrt{h w}\), where h is measured in cm, w is measured in kg, and S is measured in \(m^{2}\). Suppose that h and w are functions of t.
a. Find S'(t).
b. Show that the condition that the surface area remains constant as h and w change is wh' (t) + hw' (t) = 0.
c. Show that part (b) implies that for constant surface area, h and w must be inversely related; that is, h = C/w, where C is a constant
Questions & Answers
QUESTION:
Body surface area One of several empirical formulas that relates the surface area of a human body to the height h and weight w of the body is the Mosteller formula \(S(h, w)=\frac{1}{60} \sqrt{h w}\), where h is measured in cm, w is measured in kg, and S is measured in \(m^{2}\). Suppose that h and w are functions of t.
a. Find S'(t).
b. Show that the condition that the surface area remains constant as h and w change is wh' (t) + hw' (t) = 0.
c. Show that part (b) implies that for constant surface area, h and w must be inversely related; that is, h = C/w, where C is a constant
ANSWER:Solution 56E
Step 1 :
Given formula is
S (h,w) = ………………….. (1)
where h - height in centimeter ,W - weight in kilogram
and h and w are functions of t.
Step2 :