Written by: Akshika Jangid
Back in school, I used to just abhor mathematics simply because it was too difficult for me and I used to feel how these concepts we are studying related to practical life. The numbers didn’t add up — at least, not in life as I knew it back then. Yet slowly discovering its usefulness, I began to start looking for meaning through relatable dilemmas: How much paint covers a wall, how heavy an elevator in a tall building truly is, or, yes, how much aluminum a soda can use and why that matters. These lessons felt so unrelated, it was as if math existed just to create puzzles — not answers. But then one day, standing in the shadow of a tall lighthouse or popping open a cold soda can, I realized those odd calculations around surface areas and volumes were suddenly everywhere I looked.
Even when I am in a supermarket, those abstract problem sums suddenly become so tangible when I have to mentally calculate the price of 5 kg flour and decide what else I can buy from the remaining money. Suddenly, while being lost in a maze of supermarket aisles, soda cans blinked from the shelves and I realised that the shape of the cans’ i.e. cylinder is not just random—masterfully designed to hold the most liquid with the least metal. Engineers calculate every millimeter of surface area for the manufacturing cost and squeeze every drop of volume, making sure what lands in your hand is economical, eco-friendly, and perfectly practical. Even a small tweak to the can’s dimensions can have big impacts on sustainability and expense.
Understanding the role of Surface areas and Volumes: Brief Overview
Surface areas and volumes of different figures and solids play an important role in our day to day life. From a farmer estimating the cost of his ploughing field, deciding the no. of trees to be planted to a construction worker laying down the tiles on the floor and figuring out the price of painting the interior and exterior of the building walls; all involve the calculation of surface areas and cost per sq unit. Even when you visit a planetarium, observing the vastness of the sky, planets, stars, constellations right above your head on a big dome-like surface would have required the accurate measurements during its construction for you to have an immersive experience.
Surface areas are also involved in sciences, be it while studying habitats’ evolution and evaluating ecosystems’ functions for understanding heat transfer, phenomena like evaporation and chemical reactions or the thermal management to get energy-efficient cooling systems among many other applications. But the role of surface areas extends far beyond what we see in our daily life. Even in laboratories around the world, chemists, metallurgists, and material scientists design and produce new materials to meet specific needs , for instance when a solid state physicists study semiconductors, scientists tune semiconductor’s performance in applications ranging from microelectronics and sensing to energy conversion by modifying the surface areas through techniques like surface functionalization and by characterizing its structure using tools like scanning tunneling microscopes– tailoring them to power our information driven society.
You might have also come across terms such as the surface tension of a liquid that simply reveals their importance when studied through the lens of surface area. For eg: the pressure created inside or outside a water bubble depends on this very property, which in turn is defined by its surface area.
With the emergence of advanced technologies– from simple calculators to powerful microscopes that probe the world of nanotechnology allows us to study these surface properties with utmost clarity and remarkable precision.
Hence, Surface area and volume is not just a mathematical concept; it is a gateway to understanding nature, developing new technologies and shaping the future of science and society.
Surface Area, Volume, and the Secrets of Nature
Surface area is the total region covered by the outer surface of an object. For any three-dimensional figure, it is calculated as the sum of the areas of all its faces and bases. The surface area of a solid can play different roles depending on context like malleability of an object or the metal. For example, to a metallurgist or a goldsmith, the malleability of a metal determines whether it can be beaten into thin sheets or whether it breaks apart due to brittleness. Gold, as we know, is the most malleable metal and can be stretched or hammered into extremely thin sheets, while other metals may shatter or crack because of weaker cohesive forces that bind their particles together.
It is important not to confuse volume with mass, as they describe completely different properties of matter. Volume measures the amount of space an object occupies—in other words, the capacity of a container to hold a substance. Mass, on the other hand, relates to the quantity of matter and its density. For instance, a bag filled with cotton and another of the same size filled with safety pins may have equal volumes yet very different masses. Their volumes can be measured using the mathematical formulas we study in school.
The link between surface area and natural phenomena becomes even more fascinating when we look around in daily life. You may have noticed dew drops delicately clinging to spider webs, or tiny droplets of milk and oil forming perfect beads on a flat surface. Have you ever wondered why these drops tend to be spherical, while a drop of alcohol spreads and flattens out? The answer lies in surface tension—the property of liquids that pulls their surfaces to contract into the smallest possible area. Among all solid shapes with the same volume, the sphere has the least surface area, which is why droplets form this shape naturally.
From Shapes to Solids: Learning Beyond Formulas
To truly understand the formulas for surface area and volume, it is important to first learn about the properties of different 2‑D and 3‑D shapes, as this forms an essential part of geometry and mathematics education in primary school. In fact, 2‑D shapes serve as the foundation for constructing 3‑D figures.
A student’s ability to calculate the surface area of solids, such as prisms, develops from their knowledge of how the areas of 2‑D shapes combine to form these 3‑D objects. However, research shows that teachers often emphasize rote memorization of formulas and their direct application to problem-solving, rather than encouraging students to explore and visualize how flat shapes come together to create three-dimensional forms. When students are given opportunities to build, manipulate, and experiment with shapes, they can discover these formulas in a more meaningful and lasting way.
Thus, these concepts are fundamental to how we interact with and understand the world around us. Be it biology, engineering, environment science, medicine, business, economics and life in general, these concepts are at play in various spheres of our life.
Surface Area-to-Volume Ratio in Daily Life
Have you ever noticed that cutting vegetables into smaller pieces makes them cook faster? This happens because slicing increases their surface area, allowing heat to transfer more quickly. A clever cook in a restaurant also prefers peeling large potatoes rather than many small ones, since peeling 10 kg of large potatoes exposes less surface area compared to peeling the same weight of small ones. This demonstrates how the surface area of miniature substances, in proportion to their volume (or weight), is much larger.
We see similar effects in daily life. Freezing water in an ice tray, for example, maximizes the exposed surface area, speeding up the freezing process. Likewise, when building a fire, we start with kindling—small pieces of wood that have a high surface area-to-volume ratio—because they ignite and burn rapidly. In contrast, larger logs with a lower ratio burn more slowly, providing steady and long-lasting heat.
Biological Significance
In biology, the surface area-to-volume ratio plays a critical role in the functioning of cells and organisms. Cells are small because this ratio is optimal for absorbing nutrients and expelling waste efficiently. If a cell were much larger, its surface area would not increase enough to keep up with its growing volume, making these essential processes inefficient.
This principle also explains the design of certain organs in the human body. Our lungs, with their millions of alveoli, and our intestines, with their villi, both maximize surface area to ensure efficient gas exchange and nutrient absorption. The same concept applies to the animal kingdom. Animals in cold climates, like polar bears, tend to have a smaller surface area-to-volume ratio, helping them conserve heat. In contrast, animals in hot deserts, such as the fennec fox with its large ears, have a larger ratio to release excess body heat more effectively.
Engineering and Design
Engineers and designers constantly take surface area and volume into account when solving real-world problems. For instance, a car’s radiator relies on thin fins to maximize surface area, allowing it to dissipate heat more efficiently. Architects, on the other hand, consider both factors while designing buildings: the volume determines how much space must be heated or cooled, while the surface area controls how much heat is lost or gained through walls, windows, and roofs. Shipbuilders also face a delicate balance—while the volume of a ship’s hull determines its buoyancy, the surface area directly affects drag and overall efficiency in moving through water.
Business and Economics
In logistics, companies strive to maximize the volume of goods that can fit into shipping containers or trucks in order to minimize transportation costs. This is why packaging is often designed in cubic or rectangular forms—they make the best use of space. In manufacturing, however, the focus may shift toward surface area. Optimizing surface area can reduce the amount of raw material required, making production more cost-effective. For example, designing a product with the same internal volume but a thinner shell can significantly cut down material usage without compromising function.
Way forward: Math that shapes life
What once felt like a classroom curse is, in fact, is a life skill. From the first fizz of a soda to the dazzling glow of a city’s skyline, surface area and volume are the silent architects shaping our world. When you step outside, almost everything you touch is defined—quite literally—by the numbers you once resented. Mathematics, it turns out, isn’t about solving strange riddles on paper; it’s about unlocking the code to everyday living.
