10.8.5 Self-Check on Volumes

Tick iconExercise 9: Volume of the Earth and Moon

The mean radius of the Earth is 6,371 km and the mean radius of the Moon is 1,737 km.  Assuming that both are perfect spheres calculate the volume of each in km3, showing your answers in scientific notation and to 3 decimal places.  Then work out how many Moons could fit into the Earth.

Solutions icon

Answer

Volume of a sphere = italic four divided by italic three postfix multiplication pi prefix multiplication of left parenthesis radius right parenthesis super three

So volume of Earth equals four solidus three multiplication pi multiplication left parenthesis 6371 m right parenthesis cubed

prefix of equals 1.083 multiplication 10 super 12 times km cubed times left parenthesis to three d full stop p full stop right parenthesis

Volume of Moon equals four solidus three multiplication pi multiplication left parenthesis 1737 m right parenthesis cubed

prefix of equals 2.195 multiplication 10 super 10 times km cubed times left parenthesis to three d full stop p full stop right parenthesis

So number of Moons into the Earth equals 1.083 multiplication 10 super 12 times km cubed

prefix of 2.195 multiplication 10 super 10 times km cubed

prefix of equals 49.3

Hence the Moon could fit into the Earth approximately 49 times.

Tick iconExercise 10: How Much Water for a Typical Bath?

A bathtub measures 0.65 m wide by 1.5 m long and is 0.4 m deep. Assuming that the bathtub is a rectangular box and that it is only half filled usually, calculate the volume of water used for a typical bath in liters.

Solutions icon

Answer

Volume of a rectangular box = length multiplication width multiplication depth

Depth of water equals 0.4 m solidus two

prefix of equals 0.2 m

So volume of water equals 0.65 m multiplication 1.5 m multiplication 0.2 m

prefix of equals 0.195 m cubed

one m cubed times equals 1000 liters

So volume of water equals 0.195 multiplication 1000 l

prefix of equals 195 l

The volume of water used for a typical bath is 195 l.

10.8.4 Self-Check on Areas

10.9 Quiz Time