Quote of the Day
It is better to fail in originality than to succeed in imitation.

Figure 1: Larsen C Ice Shelf. (Source)
I just read an article about a large iceberg that will likely form in 2017 when a 5,000 km2 section of the Larsen C ice shelf (Figure 1) calves into the Antarctic Ocean. There is concern that the formation of this iceberg will remove a barrier that has been preventing the entire Larsen C ice shelf, with a total area of over 50,000 km2, from sliding into the sea. This is a massive amount of ice.
According to this article, if the land-based portion of the Larsen C ice shelf slides into the sea, sea level would rise by 10 cm. Let's try to approximate this calculation. Figure 2 shows a map of the ice thickness.
It looks like most of the ice sheet is about 650 m to 750 m thick. I will assume the average ice thickness is 700 m, which we can use to estimate the sea level rise as shown in Figure 3. I get 9 cm of sea level rise, which is close enough for a rough estimate like this.

Figure 2: Approximate Calculation of the Sea Level Rise Due to the Melting of the Larsen C Ice Shelf.
Figure 3 shows a giant rift forming along the edge of the Larsen C ice sheet, which is expected to calve off this year. The iceberg formed is expected to be one of the ten largest ever recorded.

Figure 3: Huge Rift Forming Along the Edge of the Larson C Ice Sheet. (Source)
The radius of the Earth is actually 6370 km, so your calculation is a little pessimistic. Nevertheless, the consequences of global warming for us all is well illustrated. I'm writing this from a boat sailing off the coast of Norway inside the Arctic circle. The temperature is a balmy 6 degrees centigrade and the only visible snow is on the mountain peaks.
Thanks Malcolm. I meant to write 4000 miles, not 4000 km. This means that the sea level rise is ~ 4 cm instead of 10 cm. I wonder if the original author made the same error?
mark
P.S. I find my error. I was assuming the land-based portion was the same thickness as the sea-based portion of the ice sheet. The difference is quite large. I have updated the post. Again, thanks for pointing out the issue.