High School

The body surface area of a person in square meters can be modeled by:

\[ A = \frac{\sqrt{h} \cdot \sqrt{w}}{56} \]

where:
- \( A \) is the surface area,
- \( h \) is the height of the person in inches,
- \( w \) is the weight of the person in pounds.

Use the model to find the surface area of a person who is 63 inches tall and weighs 172 pounds.

Surface area = \(\square\) m\(^2\)

Enter your next step here.

Answer :

To find the body surface area of a person using the given model, follow these steps:

1. Understand the Formula:
The formula to calculate the body surface area [tex]\( A \)[/tex] in square meters is given by:

[tex]\[
A = \frac{\sqrt{h} \cdot \sqrt{w}}{56}
\][/tex]

where:
- [tex]\( h \)[/tex] is the height in inches
- [tex]\( w \)[/tex] is the weight in pounds

2. Plug in the Values:
You are given that the height [tex]\( h \)[/tex] is 63 inches and the weight [tex]\( w \)[/tex] is 172 pounds. Substitute these values into the formula:

[tex]\[
A = \frac{\sqrt{63} \cdot \sqrt{172}}{56}
\][/tex]

3. Calculate the Square Roots:
- Calculate [tex]\(\sqrt{63}\)[/tex].
- Calculate [tex]\(\sqrt{172}\)[/tex].

4. Multiply the Square Roots:
Multiply the results from the previous step:

[tex]\[
\text{Result of step 3 multiplication}
\][/tex]

5. Divide by 56:
Finally, divide the product obtained in step 4 by 56 to find the surface area:

[tex]\[
A = \text{(Result from step 4)} \div 56
\][/tex]

Based on these steps, the calculated body surface area of the given person is approximately [tex]\( 1.86 \, m^2 \)[/tex].