Question

Mammals have approximately the same density as fresh water. (a) Find the volume in liters of a 75 kg woman and (b) the volume in cubic meters of a 121,165 kg blue whale. (Note: 1 liter = 10−3 m3 = 0.001 m3.) Round all your answers to the nearest integer.

Answer 1

(a) The volume of the woman in liters is 75 L

(b) The volume of the blue whale in cubic meters is 121 m³

Explanation:

From the question,

Mammals have approximately the same density as fresh water.

The density of fresh water is 1000 kg/m³,

∴ The density of mammals is approximately 1000 kg/m³.

Now, we will convert this to kg/L

1L = 0.001 m³

∴ 1 m³ = 1/0.001 L = 1000L

Hence, 1000 kg/m³ = 1000kg/1000L = 1 kg/L

The density of mammals is 1 kg/L

(a) To find the volume in liters of a 75 kg woman,

From the formula

Density = Mass / Volume

Then, Volume = Mass / Density

Mass of the woman = 75 kg

Density = 1 kg/L

∴ Volume = 75kg / 1kg/L = 75 L

Hence, the volume of the woman in liters is 75 L

(b) To find the volume in cubic meters of a 121,165 kg blue whale.

Using the same formula

Volume = Mass / Density

Mass = 121165 kg

Density = 1000 kg/m³

∴ Volume = 121165kg / 1000 kg/m³ = 121.165 m³ ≅ 121 m³

Hence, the volume of the blue whale in cubic meters is 121 m³.