Use the law of universal gravitacion to predict what would happen to earth if the moon were replaced with an object that had the mass of jupiter.

Vey interesting !
If the moon were replaced by something with a vastly greater mass
but at the same distance, then ...

-- The period of its revolution around the Earth would be much shorter.
That is, it would orbit the Earth in much less than 27.3 days.  We might
see it go through a complete set of phases in 2 weeks, or even 1 week.

-- The ocean tides would be much greater.  Low tides would be
much lower, and high tides would be much higher.

-- Sadly, the land tides, and the forces on the Earth's internal structure,
would also be much greater.  That means great increases in earthquake
and volcanic activity.

-- The Earth and moon both revolve around their common center of
mass. Under the current arrangement ... with the Earth having 80 times
the mass of the Moon ... that point is inside the Earth, and it looks a lot
like the Moon is orbiting a stationary Earth.
When the new body arrives to replace the lightweight Moon, that point
will be a lot closer to the new companion ... maybe even inside it. 
Then, it will look a lot like the monster is the stationary one, and the
Earth is orbiting it.
I actually don't believe that we would SEE that change, or feel it.

Yes

Multiply the 3 dimensions, assuming it is a rectangular cuboid, to get the volume in cm³ divide mass by volume to get density in g/cm³