Question

The Dubois formula relates a person's surface area, s, in meters2, to weight, w, in kg, and height, h, in cm, by (a) What is the surface area of a person who weighs 60 kg and is 160 cm tall? (b) The person in part a stays constant height but increases in weight by 0.4 kg/year. At what rate is his surface area increasing when his weight is 64 kg?

Answer 1

Answer

given,  

Dubois formula  

    $S = 0.01 w^{0.25}h^{0.75}$  

a) mass = 60 Kg  

   height = 1.6 m

     $S = 0.01 \times 60^{0.25}\times 160^{0.75}$  

          S = 1.252 m²  

   hence, surface area of a person is equal to 1.193 m² .  

b) $\dfrac{dw}{dt} = 0.4\ kg/year$  

   weight = 60 Kg  

now,  

    $\dfrac{dS}{dt} = 0.01(0.25)(\dfrac{h}{w})^{0.75}\dfrac{dw}{dt}$

    $\dfrac{dS}{dt} = 0.01(0.25)(\dfrac{160}{60})^{0.75}\times 0.4$

    $\dfrac{dS}{dt} = 0.00209\ m^2/year$