Posted by **Danny** on Thursday, December 3, 2009 at 8:25pm.

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

- Physics -
**MathMate**, Thursday, December 3, 2009 at 10:55pm
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.

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