Question

The volume of an object is 8.12 x 10–3 m3. Calculate the volume in cubic feet. (2.54 cm = 1.00 inch, 12.0 inches = 1.00 foot)

Answer 1

0.287 cubic feet

Explanation:

The volume must be converted using the conversion factors, making sure that the units properly cancel:

8.12 x 10-3 m³ x (100cm/1m)³ x (1in/2.43cm)³ x (1ft/12in)³ = 0.286 ft³

Answer 2

The volume of the object in
`ft^(3)` is
`0.2867ft^(3)`

Explanation:

Wherever we have an expression such as for example :

`2.54cm=1.00inch`

We can divide both terms to obtain a number ''1'' :

`(2.54cm)/(1.00inch)=1` or
`(1.00inch)/(2.54cm)=1`

Then, we can multiply a unit by ''1'' without change its value. The trick is to use the fractions that are equal to ''1'' in order to convert the unit.

To solve this exercise, we are going to need the following equivalence :

`1m=100cm` (I)

Working with (I) and the two equivalence between units that are given we can find the volume in cubic feet.

The volume of the object is
`(8.12).10^(-3)m^(3)`

If we work with the unit meter ''m'' and the equivalences between units ⇒

`(8.12).10^(-3)m^(3)=(8.12).10^(-3)(m.(100cm)/(1m).(1.00inch)/(2.54cm).(1.00foot)/(12.0inches))^(3)` ⇒

`(8.12).10^(-3)((100)/((2.54).(12.0))ft)^(3)=0.2867ft^(3)`

We find that the volume of the object
`(8.12).10^(-3)m^(3)` is equivalent to
`0.2867ft^(3)`