A cube of platinum of edge length 0.034 mm (density \( =21.4 \frac{\mathrm{~g}}{\mathrm{~cm}^{3}} \) ). Round your answer to 2 significant digits. mass: \( \square \mathrm{g} \)

To find the mass of the cube of platinum, we can use the formula for the volume of a cube and then multiply it by the density of platinum. Given: - Edge length of the cube = 0.034 mm - Density of platinum = 21.4 g/cm³ First, we need to convert the edge length from mm to cm to match the units of the density. Edge length in cm = 0.034 mm * (1 cm / 10 mm) = 0.0034 cm Now, we can calculate the volume of the cube using the formula: \[ \text{Volume} = \text{edge length}^3 \] \[ \text{Volume} = (0.0034 \, \text{cm})^3 \] Next, we can calculate the mass of the cube by multiplying the volume by the density of platinum: \[ \text{Mass} = \text{Volume} \times \text{Density} \] \[ \text{Mass} = (0.0034 \, \text{cm})^3 \times 21.4 \, \text{g/cm}^3 \] Let's calculate the mass of the cube of platinum. Calculate the value by following steps: - step0: Calculate: \(0.0034^{3}\times 21.4\) - step1: Convert the expressions: \(\left(\frac{17}{5000}\right)^{3}\times 21.4\) - step2: Convert the expressions: \(\left(\frac{17}{5000}\right)^{3}\times \frac{107}{5}\) - step3: Multiply the numbers: \(\frac{525691}{5\times 5000^{3}}\) The mass of the cube of platinum is approximately \(8.411056 \times 10^{-7}\) g. Rounding to 2 significant digits, the mass of the cube of platinum is approximately \(8.4 \times 10^{-7}\) g.