Question

The moon’s average density is about 3.34 grams per cubic centimeter. what is this density in units of pounds per cubic inch?

Answer 1

As per the question the average density of the moon [ω]
`= 3.34gram/cm^3`

The density of a substance is defined as mass per unit volume.Mathematically density ω =
`(mass)/(volume)`

We are asked to convert this value from
`gram/cm^3` to
`pound/inch^3`

We know that one gram is equal to .0022 pound i.e

1 gram=.0022 lb

Again one centimetre is equal to .394 inch i.e

1 cm=.394 inch

Hence density[ ω]= 3.34
`gram/cm^3`

⇒ω
`= 3.34*(0.0022lb)/([0.399inch]^(3) )`

⇒ω
`=3.34*(.0022)/(.061162984) lb/inch^3`

⇒ω
`=0.120138 lb/inch^3` [ans]

Answer 2

This problem only needs the conversion factor for grams to lbs and centimetre to inches. The conversion factor that would be used are 1 lb = 453.592 grams and 1 inch = 2.54 cm. Thus you would divide 3.34 grams with 453.592 grams then multiply it with the cube of 2.54 cm. The answer would be 0.1207 lb/in^3.