
Concept explainers
The volume of ice in Antarctica and the amount by which the water level of the world’s oceans would rise, if the ice in Antarctica were to melt completely. Also, give the portions of the Earth that will get covered by water completely. It is given that the area of Antarctica is 13 million square km and the thickness of ice cap varies from 300 m at the coast to 1800 m in the interior.

Answer to Problem 43Q
Solution:
The volume of ice in Antarctica is
Explanation of Solution
Given data:
The area of Antarctica is 13 million square kilometer or
Formula used:
The expression for volume is written as,
Here, V is the volume, A is the area and w is the width.
Density of a body is calculated as,
Here, M is mass of the body in kg and V is volume of the body in
The expression for calculating area of a sphere is written as,
Here, r is the radius of the sphere.
Explanation:
The average thickness or width of the polar ice caps can be calculated by taking the average of the thickness given for the coastal and interior regions.
Change the unit of width from m to km as,
Write the formula for volume of iceberg as,
Substitute 1.05 km for w and
Write the expression for density of water and rearrange for M.
Substitute
Only 75% of Earth’s surface is covered in water. The radius of Earth is 6378 km. Therefore, the area of the Earth that will be covered will water can be calculated as:
Substitute 6378 km for r.
In case the ice melts, the rise in the water level on earth will be calculated using formula (1). Rearrange the variables in formula (1) as shown below:
Substitute
Conclusion:
Hence, the volume of ice in Antarctica is
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