What is the estimated mass of the ice in Antarctica based on the given data?
The estimated mass of the ice in Antarctica is approximately 2.389 × 10^19 kilograms (or 2.4 × 10^19 kg to two significant figures).
Calculating the Mass of Ice in Antarctica
To estimate the mass of the ice in Antarctica, we can calculate the volume of the ice and then multiply it by the density of ice.
First, we need to find the difference in height between the average height with ice and the height without ice:
Height difference = 7500 ft - 1500 ft = 6000 ft
Next, we convert the height difference to meters:
Height difference = 6000 ft * 0.3048 m/ft = 1828.8 m
Now, we can calculate the volume of the ice using the formula:
Volume = Area * Height difference
Converting the area from square miles to square meters:
Area = 5,500,000 square miles * (2.59 km/mi)^2 * (1000 m/km)^2 = 1.42446 × 10^13 square meters
Volume = 1.42446 × 10^13 square meters * 1828.8 m = 2.60484 × 10^16 cubic meters
Finally, we multiply the volume by the density of ice to find the mass:
Mass = Volume * Density
Converting the density from g/mL to kg/m^3:
Density = 0.917 g/mL * (1000 kg/g) * (1000 mL/m^3) = 917 kg/m^3
Mass = 2.60484 × 10^16 cubic meters * 917 kg/m^3 ≈ 2.389 × 10^19 kg
Therefore, the estimated mass of the ice in Antarctica is approximately 2.389 × 10^19 kilograms (or 2.4 × 10^19 kg to two significant figures).