Answer:
The million dollar cube will be 10.79 cm tall
Step-by-step explanation:
Let the sides of the gold cube representing the tallness of the cube be s
volume of the gold cube V = s³
Then :
[tex]\mathbf{s = \sqrt[3]{V} }[/tex] --- (1)
Similarly; we know that , density ρ = mass m/Volume V
making volume the subject of the formula, then ;
V = m/ρ
Replacing that into (1) above , we have:
[tex]\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }[/tex]
Given that:
At the time, gold is selling for $1282 per troy ounce
∴ In a million-dollar cube of gold, the number of troy ounce that can be bought with a million dollar = 1000000/1282 = 780.03 troy ounce
Since 1.0000 troy ounce equals 31.1035 g
∴ 780.03 troy ounce = 780.03 × 31.1035 g
= 24261.66 g
From the tables 12.1 of Gold , the density of Gold is obtained as 19.3 g/cm³
∴
[tex]\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }[/tex]
[tex]\mathbf{s = \sqrt[3]{\dfrac{24261.66}{19.3}} }[/tex]
[tex]\mathbf{s = \sqrt[3]{1257.080829} }[/tex]
[tex]\mathbf{s = 10.79 \ cm }}[/tex]
The million dollar cube will be 10.79 cm tall
