# 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 can gain access to at least 80% of the Earth's surface, including the continents. How deep into the ocean can this submarine go? (80% of the Earth's surface is above what depth in the ocean)?**

Find 80% along the horizontal scale. Draw your vertical line until it meets the curve. Then draw a horizontal line across to meet the elevation scale. 80% meets the curve at approximately

**5.5 km below sea level**. (Your answer should be between 5 and 6 km below sea level.)

**Problem 2: You've just invented a new alloy for a submarine that can withstand underwater pressures 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 the Earth's surface is inaccessible to your ocean floor study?**

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 the 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 the Earth's surface cannot be accessed by our oceanography team!

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

Problem 4: Locate 4 km (above sea level) on the vertical scale. Draw a line to the curve on the graph and then drop a line down to the horizontal scale. This line should meet at about 2%.

**2% of the Earth's surface is above 4 km.**
**Problem 4: Most oceanic fish cannot live in depths below 4 km below sea level, and obviously can't live in areas that are above sea level. What percentage of the Earth can they occupy? that is, what percentage of the Earth's surface is between 4 kilometers below sea level and sea level?**

Draw a line down from where the curve intersects sea-level. You find that 29% of the Earth 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" and 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.

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**Go Back to the Hypsometric Curve Explanation

Go problems for you to do on your own at wamap