Question

If the density of aluminum and gold are 2.70 E3 and 193 E3 kg/m^3 respectively. How much aluminium by volume would you need in order to have the same weight as a 4.20 kg piece of gold? Number Units If this piece of gold were a cube it would have sides measuring 6.01 cm, What would the sides of the aluminum be if it were also a cube? Number Units

Answer 1

1.

Given that Weight of Aluminium = Weight of Gold

$W_{Al}=W_{Au}$

$m_{Al}*g=m_{Au}*g$

$m_{Al}=m_{Au}$

$\rho_{Al}*V_{Al}=m_{Au}$

$2.70*10^{3}kg/m^{3}*V_{Al}=4.20kg$

$2.70*10^{3}*V_{Al}=4.20$

$V_{Al}=\frac{4.20}{2.70*10^{3}}$

$V_{Al}=1.556*10^{-3}m^{3}$

ANSWER: ${\color{Red} V_{Al}=0.001556m^{3}}$

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Volume of aluminium cube, $V_{Al}=a^{3}$

$0.001556m^{3}=a^{3}$

$\sqrt[3]{0.001556m^{3}}=a$

$a=0.1159m$

ANSWER: ${\color{Red} a=11.59cm}$

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