Question

develop a mathematical model- sea level calculations
identifying key information

ice	ocean
dimensions of antarcticas ice sheet	2,000 m tall, radius ~2,100 km
need to figure out:		need to figure out:

calculate the volume of greenland ice
how can we use the information we are given to calculate the volume of the ice on greenland?
plan:

converting the thickness of the ice to kilometers:
1
volume of ice:

how much would earths sea level rise if all of greenlands ice melted into the ocean?

Explanation:

Step1: Convert Greenland ice - sheet thickness to km

Since 1 km = 1000 m, for a 1500 - m - tall ice - sheet, the thickness in km is $1500\div1000 = 1.5$ km.

Step2: Assume a simple model for volume calculation

Assume the Greenland ice - sheet can be approximated as a flat - topped shape. If we consider the area of the ice - sheet (not given in the problem, but if we just focus on the thickness and assume a large - scale approximation), and use the formula for the volume of a rectangular - prism (in a very simplified sense) $V=A\times h$. Here, if we assume the ice spreads evenly over the Earth's ocean area when melted. Let the area of the Earth's oceans $A = 3.619\times10^{8}$ km² and the height of the Greenland ice - sheet $h = 1.5$ km. The volume of the Greenland ice - sheet $V_{ice}=1.5\times3.619\times10^{8}$ km³ (this is a very simplified model).

Step3: Calculate sea - level rise

The sea - level rise $\Delta h$ is given by the volume of the melted ice divided by the area of the oceans. Using the formula $\Delta h=\frac{V_{ice}}{A_{ocean}}$. Since $V_{ice}$ (from the above step) and $A_{ocean}=3.619\times10^{8}$ km², and $V_{ice}$ (assuming a simple model with height 1.5 km) is $1.5\times3.619\times10^{8}$ km³. Then $\Delta h = 1.5$ km.

Answer:

If all of Greenland's ice melted into the ocean, the Earth's sea - level would rise by 1.5 km (assuming a very simplified model).