# What is the mass, in metric tons, of a cube of gold that is 43.8cm on each side? (1 metric ton = 1000 kg, d = 19.3 g/cm3)

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### 4 Answers

D=m/v

v = length x width x height

v = 43.8cm x 43.8cm x 43.8cm

v= 84,027.672 cm3

D = m/84,027.672cm3

19.3g/cm3 = m/84,027.672cm3

19.3 x 84,027.672 = m

mass = 1,621,734.0696g

mass = 1.62 metric tons

D=m/v

V=s^3 V=(43.8)^2 V= 84,027.672cm3

19.3g/cm3= m / 84,027.672cm3

m=1,621,734.0696g = 1.62 tons

To find the mass you must first find density, which is mass divided by volume. Volume for you cube of cold would be your side length, 43.8 cm, cubed (` ``43.8^(3)` ) which equals 84,027.672 cm^3.``

The problem has already given you the density so now you plug in the numbers and solve for mass.

` `` `` `` ``density=(mass)/(volume)`

`19.3=(mass)/(84,027.672)`

19.3 ` `* 84,027.672 = mass

mass = 1,621,734.0696 g

The mass when converted to metric tons is **1.62 tons**.

Density is mass divided by volume.

`D = m/V`

Your volume would be:

`V = s^3`

Each side length of the cube is 43.8 cm.

`V = 84027.672`

Your density is already given to you. Plug in your known values and solve for your unknown variable (mass).

`19.3 = m/84027.672`

`m = 1621734.0696 "g"`

Convert to tons using dimensional analysis.

`1621734.0696"g" = (1"kg")/(1000"g") = (1"ton")/(1000"kg") = 1.6217 "tons"`

Your final answer should have three sig figs, so your final answer is:

`m = 1.62 "tons"`