Initial Publication Date: July 19, 2011 | Revision: September 19, 2024 (see revision history: 2 events)

Hypsometric Curve: Practice Problems

The hypsometric curve from Marshak, "Earth – Portrait of the Planet," 2nd ed. p. 37.

Click on the hypsometric curve at left to open a larger version in a new window and use it to work through the problems below. I recommend you try each of these problems before looking at the solution; otherwise you won't know if you have gotten it or not. You can download a sheet with all the questions (Acrobat (PDF) 109kB Jul25 09) to help. Your answers may not be exactly the same as the ones given here because the graph is not precise. Your answers should be within a half a kilometer or 5%.

The Problems

Problem 1: You want to create a submarine that allows you to gain access to at least 80% of Earth's surface, including the continents. How deep into the ocean can this submarine go? (That is, 80% of Earth's surface is above what depth in the ocean?)

Show Problem 1 solution

Problem 2: You've just invented a new alloy for a submarine that can withstand underwater pressures up to a depth of 4.5 km below sea level. If this is the maximum depth to which an oceanographer interested in the sea floor could go, what percentage of Earth's surface is inaccessible to your ocean floor study?

Show Problem 2 solution

Find 4.5 km on the vertical axis. Draw a line horizontally until it hits the hypsometric curve. Extend a line down vertically until it crosses the horizontal axis. The value is about 60%, so you could see 60% of Earth's surface. However, we want to know how much is inaccessible. So, we need to subtract 60% from 100%.
100% – 60% = 40%.
So, 40% of Earth's surface cannot be accessed by our oceanography team!

Problem 3: Most plants cannot exist higher than 4 km above sea level. What percent of the Earth's surface is higher than this?

Show Problem 3 solution

Problem 4: Most oceanic fish cannot live in depths lower than 4 km below sea level, and obviously can't live in areas that are above sea level. What percentage of Earth can they occupy? That is, what percentage of Earth's surface is between 4 kilometers below sea level and sea level?

Show Problem 4 solution

Draw a line down from where the curve intersects sea level. You find that 29% of Earth's surface is above sea level, so 71% is below sea level. However, we want to exclude the area deeper than 4 kilometers below sea level. From the graph we find that about 53 % of the Earth is deeper than 4 km below sea level. (47% is above, so 53% must be deeper.) We want to remove this part, or subtract it, so 71% – 53% is 18%. Therefore, 18% of the Earth is below sea level but higher than 4 km below sea level.

If this makes sense to you, go on to the quiz! If it doesn't, read on.

Think about if I want to find out what portion of my class is between 5'5" tall and 5'8" tall. I can determine how many people are shorter than 5'8" and then remove the ones that are below 5'5". Then I will be left only with the students that are between 5'5" and 5'8". This is exactly what we do in this case. We see how much of the Earth is below sea level (71%) and then remove the part that is too deep (deeper than 4 km below sea level: 53%). The remainder is in the range we want.