Question

Hi im new so maybe one of you can help me understand this question, can't find it anywhere in the book.

A person weighs 723N in air and has a body-fat percentage of 29.3% .

What is the overall density of this person's body?
What is the volume of this person's body?
Find the apparent weight of this person when completely submerged in water?

So very confused

Answer 1

There are two formulas used for calculating body-fat (fraction) from density:
Brozek formula: BF =(4.57/ρ-4.142)
Siri formula is: BF = (4.95/ρ−4.50)

Take the inverse of the first one:
F=BF(ρ)=(4.57/ρ-4.142)
R1(F)=ρ=4.57/(F+4.142)
or the Siri formula:
F=BF(ρ)=(4.95/ρ-4.5)
R2(F)=ρ=4.95/(F+4.5)

For F=29.3%=0.293,
R1(F)=1.030
R2(F)=1.0327
Use the average of 1.031
Mass = 723N/9.8
=73.8 kg
Volume = mass/density
=73.8/1031 kg/m³
=0.072 m³

Apparent weight in water and neglecting density of air
= 73.8*(1.031-1)= 2.3 kg.