Question

(d) lequel a un plus grand volume: 300 g dor ou 300 g daluminium? expliquer

Explanation:

Step1: Recall the density formula

The formula that relates mass (\(m\)), volume (\(V\)) and density (\(
ho\)) is \(
ho=\frac{m}{V}\), which can be rearranged to \(V = \frac{m}{
ho}\).

Step2: Analyze the given masses

We are given that the mass of gold (\(m_{gold}\)) and the mass of aluminium (\(m_{aluminium}\)) are both 300 g, so \(m_{gold}=m_{aluminium} = 300\space g\).

Step3: Recall the densities of gold and aluminium

The density of gold (\(
ho_{gold}\)) is approximately \(19.3\space g/cm^{3}\) and the density of aluminium (\(
ho_{aluminium}\)) is approximately \(2.7\space g/cm^{3}\). So \(
ho_{gold}>
ho_{aluminium}\).

Step4: Compare the volumes

From the formula \(V=\frac{m}{
ho}\), when the mass \(m\) is constant, the volume \(V\) is inversely proportional to the density \(
ho\) (i.e., \(V\propto\frac{1}{
ho}\) for a constant \(m\)). Since \(
ho_{gold}>
ho_{aluminium}\) and \(m_{gold} = m_{aluminium}\), we can conclude that \(V_{aluminium}>V_{gold}\) (because a smaller density will result in a larger volume when the mass is the same).

Answer:

300 g of aluminium has a larger volume.