Question

As mentioned before, our asteroid is in the shape of a sphere and has a mass of 1000 kilograms. Determine the density (in grams per cubic centimeter) of this asteroid if its diameter is known to be 1.2 meters. Useful information: 1 kg = 1000 g, 1 m = 100 cm, volume of sphere = 4/3 ? r3. Remember that the radius of a sphere is equal to half its diameter. Show all of your work. (20 points)

Answer 1

Answer: $1.1052g/cm^{3}$

Explanation:

Density $D$ is a characteristic property of a material and is defined as the relationship between the mass $m$ and volume $V$ of a specific substance or material. So, the density of the asteroid is given by the following equation:

$D=\frac{m}{V}$   (1)

On the other hand, we know the asteroid has a mass $m=1000kg$ and is spherical. This means its volume is given by the following formula:

$V=\frac{4}{3}}\pi r^{3}$   (2)

Where $r=\frac{d}{2}=\frac{1.2m}{2}=0.6m$  is the radius of the sphere and is half its diameter $d$.

Knowing this, we can calculate the volume:

$V=\frac{4}{3}}\pi (0.6m)^{3}$   (3)

$V=0.904m^{3}$   (4)

Substituting (4) in (1):

$D=\frac{1000kg}{0.904m^{3}}=1105.242\frac{kg}{m^{3}}$   (5) This is the density of the asteroid, but we were asked to find it in $\frac{g}{cm^{3}}$. This means we have to make the conversion:

$D=1105.242\frac{kg}{m^{3}}.\frac{1000g}{1kg}.\frac{1m^{3}}{(100cm)^{3}}$

Finally:

$D=1.1052\frac{g}{cm^{3}}$