Question

question 4
the mass of mars, 6.40 x 10^23 kg, is about one - tenth that of the earth, and its radius, 3395 km, is about half that of earth. what is the mean density of mars in kg/m^3?
a) 9.76 x 10^2
b) 1.95 x 10^3
c) 3.90 x 10^3
d) 7.81 x 10^3

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. The volume of a sphere (assuming Mars is spherical) is $V = \frac{4}{3}\pi r^{3}$.

Step2: Identify given values

The mass of Mars $m = 6.40\times 10^{23}\text{ kg}$, and the radius $r=3395\text{ km}=3.395\times 10^{6}\text{ m}$.

Step3: Calculate volume of Mars

$V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(3.395\times 10^{6})^{3}\text{ m}^3$.
$V=\frac{4}{3}\pi\times(3.395)^{3}\times 10^{18}\text{ m}^3\approx1.631\times 10^{20}\text{ m}^3$.

Step4: Calculate density of Mars

$
ho=\frac{m}{V}=\frac{6.40\times 10^{23}}{1.631\times 10^{20}}\text{ kg/m}^3$.
$
ho\approx 3.90\times 10^{3}\text{ kg/m}^3$.

Answer:

C. $3.90\times 10^{3}$