Water has a density of 1.0g/cm3. Aperson sits in a bath 150cm in length and 90 cm width. Thw water had a depth of 60cm befor the person sat in the bath. after sitting in the bath the water level rose to 68cm.
Calculate the mass of the person, giving your answer in kg.
well, the volume of water displaces is 150*90*8 cm^3
If the person is floating, her mass is the same as the water displaced.
If the person is submerged completely, her volume is the same as that of the water. So, if you know the person's density, that can be used.
If neither, then we have nothing to go on at all.
To calculate the mass of the person, we need to determine the change in water volume before and after the person sat in the bath.
The initial volume of water in the bath can be calculated using the dimensions of the bath and the depth of the water before the person sat in it:
Volume_initial = length × width × depth_initial
= 150 cm × 90 cm × 60 cm
Next, we need to calculate the volume of water displaced (or the change in volume) after the person sits in the bath.
The change in volume of water can be determined by calculating the volume of water after the person sits in the bath and subtracting the initial volume:
Volume_change = length × width × (depth_after - depth_initial)
= 150 cm × 90 cm × (68 cm - 60 cm)
Now, since water has a density of 1.0 g/cm³, we can calculate the mass of the water displaced (and indirectly the mass of the person) using the equation:
Mass = Density × Volume_change
Substituting the known values, we can calculate the mass of the person:
Mass = 1.0 g/cm³ × (150 cm × 90 cm × (68 cm - 60 cm))
Finally, to convert the mass from grams to kilograms, we divide the mass by 1000:
Mass (in kg) = Mass (in g) / 1000
Now you can calculate the mass of the person by plugging in the values into the equation.