In a total-immersion measurement of a woman's density, she is found to have a mass of 63 kg in air and an apparent mass of 0.0975 kg when completely submerged with lungs almost totally empty.
a. what mass, in kg, of water does she displace?
b. what is her volume in m^3?
c. what is her average density in kg/m^3?
d. if her lung capacity is 1.75 l, is she able to float without treading water with her lungs filled with air? assume the density of air is 1.29 kg/m3.

Explanation:

A) mass of displaced water = loss of mass in water = 63 - .0975 = 62.9025 kg

B) her volume = volume of displaced water

= mass of displaced water / density of water = 62.9025 / 1000 m³.

= 62.9025 x 10⁻³ m³

C) her average density = her mass / her volume = 63 / 62.9025 x 10⁻³

= 1.00155 x 10³ kg / m³

D) lung capacity = 1.75 L = 1.75 x 10⁻³ m³

buoyant force created by air in the lungs = 1.75 x 10⁻³ ( 1000- 1.29 ) =  1.74 kg

As it is more than 0.0975 kg , the apparent weight  in water so woman will float in water .