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)`

Step-by-step 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=(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=(4)/(3)}\pi r^(3)` (2)

Where
`r=(d)/(2)=(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=(4)/(3)}\pi (0.6m)^(3)` (3)

`V=0.904m^(3)` (4)

Substituting (4) in (1):

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

`D=1105.242(kg)/(m^(3)).(1000g)/(1kg).(1m^(3))/((100cm)^(3))`

Finally:

`D=1.1052(g)/(cm^(3))`