Question

question 1-18 a cube of an unknown metal has a side length of 3.45 cm. if the sample is found to have a mass of 71.25 g, find the density (in g/cm³) of the cube. 1.74 20.7 0.0484 245.8

Explanation:

Step 1: Recall the formula for density and volume of a cube

Density ($
ho$) is given by the formula $
ho = \frac{m}{V}$, where $m$ is the mass and $V$ is the volume. For a cube, the volume ($V$) is given by $V = s^3$, where $s$ is the side length of the cube.

Step 2: Calculate the volume of the cube

The side length ($s$) of the cube is $3.45\ \text{cm}$. So, we calculate the volume as follows:
$$V = s^3=(3.45\ \text{cm})^3$$
First, calculate $3.45\times3.45 = 11.9025$, then multiply by $3.45$: $11.9025\times3.45 = 41.063625\ \text{cm}^3$

Step 3: Calculate the density

We know the mass ($m$) is $71.25\ \text{g}$ and the volume ($V$) is $41.063625\ \text{cm}^3$. Using the density formula:

$$ ho=\frac{m}{V}=\frac{71.25\ \text{g}}{41.063625\ \text{cm}^3}$$

Divide $71.25$ by $41.063625$: $\frac{71.25}{41.063625}\approx1.74\ \text{g/cm}^3$

Answer:

1.74