Questions: Fluid Mechanics Mars has a mass of 6.42 * 10^23 kg, and a radius of 3.40 * 10^6 m. What is the average density of Mars? (Unit = kg / m^3 )

Solution Steps

To find the average density, we first need to calculate the volume of Mars. Mars is approximately spherical, so we use the formula for the volume of a sphere:

\[ V = \frac{4}{3} \pi r^3 \]

Given the radius \( r = 3.40 \times 10^6 \, \text{m} \):

\[ V = \frac{4}{3} \pi (3.40 \times 10^6)^3 \]

Simplify the expression for the volume:

\[ V = \frac{4}{3} \pi (3.40 \times 10^6)^3 = \frac{4}{3} \pi (3.40^3 \times 10^{18}) \]

\[ V = \frac{4}{3} \pi (39.304 \times 10^{18}) \]

\[ V \approx 1.654 \times 10^{20} \, \text{m}^3 \]

The average density \( \rho \) is given by the mass divided by the volume:

\[ \rho = \frac{m}{V} \]

Given the mass \( m = 6.42 \times 10^{23} \, \text{kg} \) and the volume \( V \approx 1.654 \times 10^{20} \, \text{m}^3 \):

\[ \rho = \frac{6.42 \times 10^{23}}{1.654 \times 10^{20}} \]

\[ \rho \approx 3881 \, \text{kg/m}^3 \]

Final Answer