How do you calculate approximate sea level rise if the entire east and west Antarctic ice sheets melted?

Question

The Antarctic ice sheets (East and West) have a combined area of 13.9 million km² and a total estimated volume of 26.5 million km³. If both ice sheets completely melted, the 26.5 million km³ of ice would be added to the oceans, causing sea level to rise.

Given the total area of the world’s oceans = 361.9 million km², calculate the eustatic (global) sea level rise that would be seen if all of the Antarctic ice sheets melted rapidly. Show your workings and give your answer in meters.

Answer 1

So you set this up like an equation with what you know and the key is to solve this you must assume the ocean area doesn't change, but first lets just start by defining some things.

So volume is base x width x height, so essentially volume of oceans b_ow_o= 361.9 mil km² and we know the volume of the current ocean is 361.9 mil km² x h_ocean

I'll also write it as b_ow_oh_o= 361.9 mil km² x h_o

We know the new sea level is h_o+h_rise and assuming sea area doesn't change we can make the equation.

b_ow_o(h_o+h_rise)=361.9 mil km² x h_o + 26.5 mil km³

or for just ease of writing

b_ow_o(h_o+h_rise)= b_ow_oh_o + 26.5 mil km³

then you solve for h_rise

b_ow_oh_o+b_ow_oh_rise= b_ow_oh_o + 26.5 mil km³

b_ow_oh_rise=b_ow_oh_o - b_ow_oh_o + 26.5 mil km³

b_ow_oh_rise=26.5 mil km³

h_rise=26.5 mil km³/b_ow_o

h_rise=26.5 mil km³/361.9 mil km² the answer should be in km so here we can check that the units of the answer will be in km since km³/km² = km

h_rise=0.07322 km

h_rise=0.07322 km x 1000m/km = 73.2m

relative sea level rise from all the ice sheets melting would be about 73.2m