A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass of the sample to be 20.0 g . The rectangular block is \( 2.00 \mathrm{~cm} \times 3.00 \mathrm{~cm} \times 1.40 \mathrm{~cm} \). Calculate the density \( \left(\right. \) in \( \left.\mathrm{g} / \mathrm{cm}^{3}\right) \). Express your answer to the correct number of significant figures. Answer: \( \square \mathrm{g} / \mathrm{cm}^{3} \)

To find the density, we first need to calculate the volume of the rectangular block. The formula for the volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] Substituting the values, we have: \[ V = 2.00 \text{ cm} \times 3.00 \text{ cm} \times 1.40 \text{ cm} = 8.40 \text{ cm}^3 \] Next, we can calculate the density \( \rho \) using the formula: \[ \rho = \frac{\text{mass}}{\text{volume}} \] Plugging in the mass and volume, we find: \[ \rho = \frac{20.0 \text{ g}}{8.40 \text{ cm}^3} \approx 2.38 \text{ g/cm}^3 \] Since our mass is recorded to three significant figures, we will express the density as well to three significant figures: Answer: \( 2.38 \, \text{g/cm}^3 \)