To solve this problem, we need to calculate the density of the block of metal. Density ($\rho$) is given by the formula:

$\rho = \frac{\text{mass}}{\text{volume}}$

Step 1: Determine the volume

The volume ($V$) of a rectangular block is calculated as:

$V = \text{width} \times \text{length} \times \text{height}$

Given:

• Width = $3.2 \, \text{cm}$
• Length = $17.1 \, \text{cm}$
• Height = $3.8 \, \text{cm}$

$V = 3.2 \times 17.1 \times 3.8$

$V = 208.512 \, \text{cm}^3$

Step 2: Convert the mass to grams

The given mass is $1.4 \, \text{kg}$. Since $1 \, \text{kg} = 1000 \, \text{g}$:

$\text{Mass} = 1.4 \times 1000 = 1400 \, \text{g}$

Step 3: Calculate the density

Using the formula for density:

$\rho = \frac{1400}{208.512}$

$\rho \approx 6.71 \, \text{g/cm}^3$

Step 4: Express the answer to two significant figures

Rounding $6.71$ to two significant figures:

$\rho = 6.7 \, \text{g/cm}^3$

Final Answer:

The density of the metal is $\mathbf{6.7 \, \text{g/cm}^3}$.

Would you like a more detailed explanation or have any questions? Here are 5 related questions for practice:

1. How would the density change if the mass of the block was halved?
2. What is the significance of expressing the density in two significant figures?
3. Convert the density $6.7 \, \text{g/cm}^3$ into $\text{kg/m}^3$.
4. If the block were submerged in water, would it float or sink? Why?
5. What is the relationship between volume, mass, and density in physical systems?

Tip: Always ensure that units are consistent when solving problems involving physical quantities.