Final answer:
To find the mass of Deimos, we use its density and diameter to calculate its volume and then use the formula M = D * V, where M is the mass, D is the density, and V is the volume.
Step-by-step explanation:
To find the mass of Deimos, we need to calculate its volume first. Using the formula for the volume of a sphere, V = (4/3)πr³, we can find the volume.
Given that the diameter of Deimos is 13 km, the radius would be half of that, which is 6.5 km or 6500 m.
Plugging this value into the formula, we get V = (4/3)π(6500³) m³.
Now, the density of Deimos is given as 2 g/cm³. To convert this to kg/m³, we need to multiply by 1000. So the density becomes 2000 kg/m³.
To find the mass, we can use the formula D = M/V, where D is the density, M is the mass, and V is the volume. Rearranging the formula, we get M = D * V.
Substituting the values, we have M = 2000 kg/m³ * (4/3)π(6500³) m³.
Calculating this expression will give us the mass in kg.