Question

The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. BSA√(wh/3600)A. weight = 72 kg, BSA = 1.9 Calculate the height of the person.B. Using this model, estimate the weight of a person who is 163 cm tall and whose BSA is 2.2

Answer 1

The formula in getting the body surface area according to Mosteller is:

`BSA=\sqrt[]{(weight(kg)* height(cm))/(3600)}\text{ }`

Since the weight and BSA are already given in the question, let's plug in the value of the weight and BSA in the formula above.

`1.9=\sqrt[]{(72* h)/(3600)}`

To solve the height, here are our steps:

1. Square both sides of the equation.

`\begin{gathered} (1.9)^2=(\sqrt[]{(72h)/(3600)})^2_{} \\ 3.61=(72h)/(3600) \end{gathered}`

2. Cross-multiply.

`\begin{gathered} 3.61*3600=72h \\ 12996=72h \end{gathered}`

3. Divide both sides by 72.

`\begin{gathered} (12996)/(72)=(72h)/(72) \\ 180.5=h \end{gathered}`

Hence, the height of the person having a BSA of 1.9 and a weight of 72kg is 180.5 cm or 181 cm when rounded up to whole number.

On the other hand, to estimate the weight of the person given height in cm and BSA, we can derive the formula we used above and solve for the weight. The formula will be:

`w=\frac{(BSA)^2*3600\text{ }}{h}`

If the height is 163 cm and BSA = 2.2, to solve for the weight, plug in those values to the weight's formula above.

`w=((2.2)^2*3600)/(163)`

Then, solve.

`\begin{gathered} w=(4.84*3600)/(163) \\ w=(17424)/(163) \\ w=106.8957 \\ w\approx107kg \end{gathered}`

Hence, the weight of the person having a BSA of 2.2 and height of 163 cm is approximatey 107 kg.