Why should the countries even if not around the Ring of Fire be alarmed or concerned about the activities on the Ring of Fire?

Answer 1

The main concerns associated with the Ring of Fire are volcanoes, earthquakes and tsunamis. All of these can impact countries far beyond the borders where the events take place.

1. Earthquakes - while most of the damage from earthquakes is very local, the impact of the damage can be global. A large quake in Japan that destroyed a computer memory factory led to a shortage of RAM chips globally that caused computer prices to spike for months afterward. Plans for more nuclear reactors were shelved when a nuclear plant in Japan suffered a meltdown during a large quake and with the associated tsunami.
2. Volcanoes - most volcano damage is local, but truly large volcanic eruptions impact entire regions and even may have global impacts. Jets cannot fly safely through volcanic ash clouds, which may extend hundreds of kilometers from the volcano. Ash and sulfur aerosols from large eruptions that make it up into the stratosphere can circle the globe and shade the planet from incoming sunlight, causing global temperatures to fall by a substantial amount... even enough to cause crop failures on the other side of the planet.
3. Tsunamis - A large tsunami can travel for thousands of kilometers before crashing onto shorelines far away from the Ring of Fire. The terrible Boxing Day tsunami from an earthquake in Indonesia impacted shorelines very far away with devastating results to life and property.
4. Humanitarian concerns - The world cannot turn its back when others are in need. Well, it can, but that's just not right and produces more problems than it would if it lent a helping hand. What goes around comes around.