Questions: Cubes are three-dimensional square shapes that have equal sides. What is the density of a cube that has a mass of 12.6 g and a measured side length of 4.1 cm? (Density: D = m/v) .1828 g / cm^3 .3254 g / cm^3 3.073 g / cm^3 68.92 g / cm^3

Cubes are three-dimensional square shapes that have equal sides. What is the density of a cube that has a mass of 12.6 g and a measured side length of 4.1 cm? (Density: D = m/v)

.1828 g / cm^3

.3254 g / cm^3

3.073 g / cm^3

68.92 g / cm^3

Transcript text: Cubes are three-dimensional square shapes that have equal sides. What is the density of a cube that has a mass of 12.6 g and a measured side length of 4.1 cm ? (Density: $D=\frac{m}{v}$ ) $.1828 \mathrm{~g} / \mathrm{cm}^{3}$ $.3254 \mathrm{~g} / \mathrm{cm}^{3}$ $3.073 \mathrm{~g} / \mathrm{cm}^{3}$ $68.92 \mathrm{~g} / \mathrm{cm}^{3}$

Solution

Solution Steps

Step 1: Calculate the Volume of the Cube

The volume $ V $ of a cube is given by the formula: \[ V = \text{side length}^3 \] Given the side length is 4.1 cm: \[ V = (4.1 \, \text{cm})^3 = 4.1^3 = 68.921 \, \text{cm}^3 \]

Step 2: Calculate the Density

The density $ D $ is given by the formula: \[ D = \frac{m}{V} \] where $ m $ is the mass and $ V $ is the volume. Given the mass $ m = 12.6 \, \text{g} $ and the volume $ V = 68.921 \, \text{cm}^3 $: \[ D = \frac{12.6 \, \text{g}}{68.921 \, \text{cm}^3} = 0.1828 \, \text{g/cm}^3 \]