- Gold has a mass of 50 Kg , occupying a volume of $$ 10 \mathrm{~cm}^{\wedge} 3 $$ - Calculate the density

Question

UpStudy AI · Accepted Answer

Given:

- Mass: $$ m = 50 \, \mathrm{kg} $$
- Volume: $$ V = 10 \, \mathrm{cm}^{3} $$

**Step 1. Write the definition of density.**

The density $$ \rho $$ is defined by

$$
\rho = \frac{m}{V}.
$$

**Step 2. Convert the volume from cubic centimeters to cubic meters.**

Since

$$
1 \, \mathrm{cm}^{3} = 10^{-6} \, \mathrm{m}^{3},
$$

the volume in cubic meters is

$$
V = 10 \, \mathrm{cm}^{3} = 10 \times 10^{-6} \, \mathrm{m}^{3} = 10^{-5} \, \mathrm{m}^{3}.
$$

**Step 3. Calculate the density using consistent units.**

Substitute the values into the density formula:

$$
\rho = \frac{50 \, \mathrm{kg}}{10^{-5} \, \mathrm{m}^{3}}.
$$

Perform the division:

$$
\rho = 50 \times 10^{5} \, \mathrm{kg/m}^{3} = 5 \times 10^{6} \, \mathrm{kg/m}^{3}.
$$

**Final Answer:**

The density of gold is

$$
\boxed{5 \times 10^{6} \, \mathrm{kg/m}^{3}}.
$$
The density of gold is $$ 5 \times 10^{6} \, \mathrm{kg/m}^{3} $$.

- Gold has a mass of 50 Kg , occupying a volume of \( 10 \mathrm{~cm}^{\wedge} 3 \) - Calculate the density