Shield volcanoes are shaped something like flattened cones. The volume of a cone is equal to the area of its base multiplied by one-third of its height. The largest volcano on Mars, Olympus Mons, is \(27 \mathrm{km}\) high and has a base diameter of \(550 \mathrm{km}\). Compare its volume with that of Earth's largest volcano, Mauna Loa, which is \(9 \mathrm{km}\) high and has a base diameter of \(120 \mathrm{km}\)

Olympus Mons is the largest volcano in the solar system and is located on Mars. It towers at a height of 27 kilometers, making it nearly three times as tall as Mount Everest. With a base diameter of 550 kilometers, Olympus Mons covers an area similar in size to the state of Arizona.
One of its most distinctive features is the shield-like shape, resembling a flattened cone. This shape is typical for shield volcanoes, which have gently sloping sides created by low-viscosity lava flows.
The significance of Olympus Mons goes beyond its size; it provides insights into volcanic activity and geological processes on Mars. Understanding such massive volcanic structures helps scientists learn more about the planet's history and potential for past habitability.

Mauna Loa is the largest volcano on Earth, located in Hawaii. It stands 9 kilometers tall and has a base diameter of 120 kilometers. Like Olympus Mons, Mauna Loa is a shield volcano, formed from numerous lava flows over hundreds of thousands of years.
Mauna Loa's substantial size impacts the local environment. The volcano’s activity affects weather patterns, ecosystems, and even ocean currents. Due to its active nature, studying Mauna Loa is crucial for volcano monitoring and disaster preparedness.
Despite being much smaller than Olympus Mons, Mauna Loa provides valuable insights into shield volcanoes on Earth, contributing to our understanding of planetary geology.

The volume of a cone is determined by the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height.
This formula helps represent the three-dimensional space that the cone occupies. In this context, shield volcanoes can be roughly modeled as cones to compare their volumes.
For Olympus Mons, the base radius is 275 kilometers and the height is 27 kilometers. For Mauna Loa, the base radius is 60 kilometers and the height is 9 kilometers. Using the volume formula, we can calculate the volumes of these massive structures for comparison.

To calculate the volume of Olympus Mons, we first determine its base radius:\[ r = \frac{550}{2} = 275 \, km \] Then, substitute into the volume formula:\[ V = \frac{1}{3} \pi (275)^2 (27) \]\[ V = \frac{1}{3} \pi (75625)(27) \]\[ V = \frac{1}{3} \pi (2041875) \]\[ V = 680625 \pi \approx 2138730 \, km^3 \]
For Mauna Loa, the base radius is calculated as:\[ r = \frac{120}{2} = 60 \, km \]Then, substitute into the volume formula:\[ V = \frac{1}{3} \pi (60)^2 (9) \]\[ V = \frac{1}{3} \pi (3600)(9) \]\[ V = \frac{1}{3} \pi (32400) \]\[ V = 10800 \pi \approx 33929 \, km^3 \]
These calculations demonstrate the substantial difference in volume between Olympus Mons and Mauna Loa.

Planetary geology studies the geological features of celestial bodies such as planets and moons. Shield volcanoes like Olympus Mons and Mauna Loa provide critical information in this field.
By examining volcanic structures, scientists can infer the geological history and inner workings of a planet. For instance, the size and shape of Olympus Mons suggest extensive volcanic activity and a period of significant geological change on Mars.
Planetary geology's importance extends to understanding surface processes, potential resources, and even the history of water and life on other planets. Learning about volcanoes on Earth and other planets enhances our knowledge of the solar system and the dynamic processes shaping it.