Question

The base of the volcano Mauna Loa is about \(5,000 \mathrm{~m}\) below sea level. The total height of the volcano is \(9,170 \mathrm{~m}\). What percentage of the volcano is above sea level? Below sea level?

Short answer

Approximately 45.47% is above sea level, and 54.53% is below sea level.

Step-by-step solution

Understand the Total Height

First, identify the total height of the volcano, including both the part below and the part above sea level. We know the base is 5000 meters below sea level and the top part is 9170 meters high in total.

Calculate Height Above Sea Level

The part of the volcano above sea level is the total height minus the part below sea level. \[ ext{Height above sea level} = 9170 ext{ m} - 5000 ext{ m} = 4170 ext{ m}\]

Calculate Percentage Above Sea Level

To find the percentage of the volcano that is above sea level, divide the height above sea level by the total height and then multiply by 100.\[ ext{Percentage above sea level} = \left( \frac{4170}{9170} \right) \times 100 \approx 45.47\%\]

Calculate Percentage Below Sea Level

Similarly, to find the percentage of the volcano that is below sea level, divide the height below sea level by the total height and then multiply by 100.\[ ext{Percentage below sea level} = \left( \frac{5000}{9170} \right) \times 100 \approx 54.53\%\]

Key concepts

Understanding Percentage Calculation

Calculating a percentage is a crucial math skill used to express any number as a part of a whole. When you're asked to find a percentage, you're essentially discovering how much one number is out of another, in terms of 100 units. Here's a simple way to think about it:

• Identify the "part" you're interested in.
• Determine the "whole" of which this part is a portion.
• Divide the part by the whole.
• Multiply the result by 100 to convert it to a percentage.

For example, when calculating the percentage of Mauna Loa that is above sea level, the part is the height above sea level (4170 m) and the whole is the total height of the volcano (9170 m). The formula to find the percentage is:\[\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\]This process allows you to easily determine what portion of anything you're examining makes up, compared to its entire size or quantity.

Mauna Loa - The Giant Volcano

Mauna Loa is one of the world's largest volcanoes, located on the Big Island of Hawaii. Its enormity is staggering; it extends from 5,000 meters below sea level to its summit which reaches a total of 9170 meters above sea level. This gives us a unique opportunity to appreciate how much of a geological giant it actually is. Since the volcano's base begins deep below the ocean, this hidden part of Mauna Loa remains beneath the surface, unseen by the naked eye.
Understanding these figures helps us to envision the volcano in its full scale, allowing us to calculate and appreciate the proportions of Mauna Loa that lie above and below the ocean surface.

Exploring Above Sea Level

"Above sea level" refers to the part of any landform, like our volcano Mauna Loa, that rises from the surface of the water into the air. In this context, Mauna Loa's section above sea level can be visualized as the visible mountainous section that towers above the Hawaiian land.
The height above sea level is calculated by subtracting the base of the volcano that is submerged beneath the sea from the overall measured height. This gives you the height that physical structures and landscapes have over the water level. For Mauna Loa, this part is 4170 meters high.
This concept is crucial not just for geological studies, but also for navigation, aviation, and even planning habitable zones, as factors like climate, vegetation, and human activity vary significantly with elevation.

Understanding Below Sea Level

The term "below sea level" often refers to any part of a geographical formation that is submerged beneath the surface of the ocean. For Mauna Loa, this means its base starts at 5,000 meters beneath the ocean's surface.
When it comes to volcanoes like Mauna Loa, understanding what lies below sea level is critical for geological studies. This underwater portion is still a significant part of the structure and must be considered when estimating its total size or evaluating its potential impacts.

• Seafloor features play roles in ocean currents.
• Structures at these depths endure immense pressure.

Moreover, it emphasizes the greatness of formations that may seem less impressive from the surface, reminding us that much of Earth's wonders are hidden away from plain view.