Question

A swimmer finds that she just floats in water. If she weighs 70

kg what is her volume (ρwater = 1×103 kg m−3)?

Answer 1

Answer:
`0.07 m^(3)`

Step-by-step explanation:

Density
`\rho` is a physical characteristic property of matter that establishes a relationship between the mass
`m` of a body or substance and the volume
`V` it occupies. Mathematically is expressed as:

`\rho=(m)/(V)` (1)

We already know the mass of the swimmer, which is
`m=70 kg` and the density of water
`\rho=1(10)^(3) kg/m^(3)`.

The volume
`V` can be found t by the Archimedes' Principle, which states the following:

A body totally or partially immersed in a fluid at rest (water in this case), experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

Hence, the volume of the swimmer is equal to the volume her body displaces. This means we only a have to isolate
`V` from (1):

`V=(m)/(\rho)` (2)

`V=(70 kg)/(1(10)^(3) kg/m^(3))` (3)

Finally:

`V=0.07 m^(3)}`