Question

What is the mass of water required to fill a circular hot tub 2.6 m in diameter and 1.5 m deep? Answer in units of kg.

Answer 1

The volume of the hot tub is that of a cylinder:

`V=\pi r^(2)h`

The height is 1.5 m
The radius is half the diameter, which is 1.3 m

So we get

`V=\pi(1.3)^(2)(1.5)\approx7.964 m^(3)`

The density of water is 1 g/cm³

Convert to kg/m³:


`(1\ g)/(1\ cm^(3))*(1\ kg)/(1000\ g)*(100^(3)\ cm^(3))/(1\ m^(3))=(10^(6))/(10^(3))\ kg/m^(3)=1000\ kg/m^(3)`

The mass of the water is Volume*density:

`7.964\ m^(3)*1000\ kg/m^(3)=7964\ kg`

So 7964 kg of water are needed to fill the tub.