The core is necessary for a star's existence, it's the engine that keeps it from collapsing. When this engine runs out of fuel or its fuel vanishes, gravity overcomes and contracts the star until matter from the radiative zone is compressed enough to start fusing hydrogen again to counterbalance gravity.
core and radiation
If the core of the sun didn't exist we would be in some sort of weird parallel universe where the laws of physics were radically different. If you somehow managed to magically remove the core of the sun from existence, everything outside the core would collapse into the center of your (now hollow) sphere and form a new core and your sphere would be smaller. Depending on how much mass you removed, Earth's orbit might be screwed up enough to send us either flying off into space (so that we freeze to death, very bad) or hurtling into the sun (planet would be incinerated, also bad). You could also cause a massive decrease in the amount of heat the sun would be giving off. Either way, should you happen to gain the above mentioned magical powers, unless you are also immortal and don't mind having no one to talk to for eternity I would highly recommend against using them. =)
it would increase
it can not burn down a town hudave
we would die
core and radiation
If you are asking where does solar nuclear fusion take place, then that would be at the core of stars.
It is a very unlikely scenario but if it were to happen, that poor planet would be vaporized by the Suns' immense size and power. If there were to be a planet that was bigger than the Sun then both of them would be vaporized or the Sun would survive but be severely damaged and might explode because of the impact.
The core just means the centre. Therefore, the core of the Sun is in the centre of the Sun.
If the core of the sun didn't exist we would be in some sort of weird parallel universe where the laws of physics were radically different. If you somehow managed to magically remove the core of the sun from existence, everything outside the core would collapse into the center of your (now hollow) sphere and form a new core and your sphere would be smaller. Depending on how much mass you removed, Earth's orbit might be screwed up enough to send us either flying off into space (so that we freeze to death, very bad) or hurtling into the sun (planet would be incinerated, also bad). You could also cause a massive decrease in the amount of heat the sun would be giving off. Either way, should you happen to gain the above mentioned magical powers, unless you are also immortal and don't mind having no one to talk to for eternity I would highly recommend against using them. =)
it would increase
it can not burn down a town hudave
The sun would win.
It would melt.
the sun's core is the hottest part of the sun
The core can't "die" but I suppose you mean if the fusion reaction were to suddenly stop (and not be able to start again). Well, since the fusion is what keeps the sun supported, it would collapse on itself and create a mini super nova (I say "mini" because the sun is not big enough to do this on it's own). This won't happen because of the suns small size. What will happen in several billion years, is that the helium will start to form carbon, oxygen, and other heavier elements. This change in the core reaction will cause the sun to turn red and expand. This outer layer will slowly expand out, leaving a small white dwarf (which will eventually turn into a red dward, then a black dwarf).
death