10.4  In what ways do planetary rings differ from moon?  In what ways are they similar?

Both orbit a larger mass and they are made of the same materials (rock and/or ice).  A moon, however, is self-gravitating and all of it's material is in a single orbit.  Ring particles are each in a separate orbit around the parent planet.
 

10.5  Astronomers once thought that Saturn's rings were a solid disk.  Explain why this would not be physically possible.

The inner part of the ring would want to rotate faster than the outer part (Kepler's third law), so a solid disk would be torn apart.
 

10.8  Explain the process that drives volcanism on Io.

Jupiter exerts a huge tidal effect on Io.  In the absence of other influences, Io's bulge would always point toward Jupiter and nothing interesting would be happening on Io.  However, there are other moons nearby and their gravitational effects keep Io's orbit elliptical, causing Io to rotate back and forth through its bulge.  The friction heats Io up.
 

10.10  Discuss evidence that supports the idea that Europa might have a subsurface ocean of liquid water.
 
Ice on Europa's surface is broken into pieces that could be fit back together like a jigsaw puzzle.  It looks like ice in the Arctic which is floating on liquid water.  The liquid on Europa could be water or something else (such as carbon dioxide).

10.18  Planetary scientists have estimated that Io's extensive volcanism could be covering the moon's survace with lava and ash to an average depth of up to 3 mm per year.

a.  Io's radius is 1815 km.  If we model Io as a sphere, what are its surface area and volume?

b.  What is the volume of volcanic material deposited on Io's surface each year?

c.  How many years would it take for volcanism to do the equivalent of depositing Io's entire volume on its surface?

d.  How many times might Io have "turned inside out" over the age of the solar system?
 

a.   The surface area of Io is 4 x pi x R² = 4.23 x 10¹³ m².   It's volume is 4/3 x pi x R³ = 2.6 x 10¹⁹ m³.

b.  The volume is the surface area times the depth = 4.23 x 10¹³ m² x  0.003 m = 1.3 x 10¹¹ m³ per year.

c.  Divide the volume of Io by the volume deposited = 2.6 x 10¹⁹ m³ / 1.3 x 10¹¹ m³  = 2 x 10⁸ years.

d.  The Solar System is about 4.5 billion years old.  If Io has been at this for 4 billion years, at the same rate, it has turned itself inside out about 20 times.