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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sciftw's profile pic

sciftw | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

ccbbrenes's profile pic

ccbbrenes | eNotes Newbie

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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

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

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.

ayl0124's profile pic

ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

Posted on

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"`

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