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You win the lottery and decide to impress your friends by exhibiting a million-dollar cube of gold. At the time, gold is selling for $1282 per troy ounce , and 1.0000 troy ounce equals 31.1035 g. How tall would your million-dollar cube be?

Short Answer

Expert verified

The height of gold cubes purchased using million dollar is 10.79 cm .

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The selling price of gold is, p = 1282 dollar/troy ounce
  • The value of one troy ounce is, 1troy ounce = 31.1035 g
02

Concept/Significance of volume of cube

A cube is made up of six squares that are all joined to make a solid. A cube's volume is always equal to the length of one side "cubed ," or L x L x L.

03

Determination of the height of million-dollar cube.

The troy bought with one million can be given by,

10000001282/troy ounce=780.03troy ounces

The mass of the gold is given by,

m=1000000128231.1035g=24261.70g

The volume of the cube of gold is given by

V=mp 鈥(颈)

Here, m is the mass of gold troy and pis he density of gold whose value is 19.3g/cm3.

The volume of cube can also be expressed as,

V=a3 鈥(颈颈)

Here, a is the side of cube.

Equate equation (i) and (ii)

[A1]This should be done in next step 4.

a3=ma=m3

Substitute values in the above equation.

a=24261.70g19.3g/cm33=10.79cm

Thus, the height of gold cubes purchased using million dollar is 10.79 cm.

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