Any solid object or 3D figure has a surface area. This is the total sum that is found by adding up the area of all its sides. For example, a cylinder has 3 sides:
- A rectangle (represented by the wall of the cylinder)
- 1 circle on one side
- 1 circle on the other side
To get the surface area, you must get the separate areas of each side and add them all up.
You can obtain the surface area of any solid figure whether its surface is irregular, curved, or straight like a cuboid.
Some common figures that have a surface area include:
- Hemisphere (half sphere)
Worked Example of a surface area
Let us calculate the surface area of a cube. If its dimensions are 4m x 4m x 4m (width x height x length), its surface area can be found in the following way:
The area of one side is: 4m x 4m = 16m²
A cube has 8 sides. Since all 8 sides measure 4m x 4m, each of them has the same area of 16m². Therefore, the surface area of a cube is the total area of all 8 faces (16m² x 8= 128m²)
Since we always calculate the area using 2 dimensions (e.g., width x height), the surface area is always given in units followed by the superscript for squared (m²)
This is different from the volume which is calculated using 3 dimensions (length x width x height) to give the units followed by the superscript for cubed (m³)
Here are 8 real life examples of surface area:
1. Determining Amount Of Paint Used
Knowing the surface area of any object helps to estimate how much paint you will need to paint it.
For example, by calculating the floor and wall surface areas of a swimming pool or a room, you can have a good picture of the paint needed.
2. Angle Of Sunlight Or Radiation To The Earth’s Surface
Different areas of the earth’s surface lie at different angles to the incoming sunlight.
For example, the equator region lies directly under the sun so that the sun’s rays are almost perpendicular to it.
This causes the equator region to receive more heat than other areas since more radiation is focused on a smaller area.
3. Quantity Of Wrap Covering Material
Many items such as gift boxes needed to be wrapped with special packaging.
By calculating the surface area of the box, we can estimate the amount of wrapping material needed.
4. Making A Fire
If you want to create a bigger fire when you are out camping, break up your fuel (wood) into smaller pieces.
This increases the surface area of the wood so that more oxygen comes into contact with it. This makes combustion reactions (burning) easier and faster.
Twigs and splinters have a higher surface area, so they burn more readily than logs.
5. Fins For Cooling Engine
The casing of air-cooled engines (as opposed to liquid-cooled engines) are usually fitted with fins to increase surface area. For example, old-type motorcycles have fins.
It leads to faster dissipation of heat to the surroundings due to the increased surface area.
Engines need cooling to prolong their life and function.
Overheating also causes other unwanted effects such as misfiring, overheating, knocking, and damage to pistons.
6. Temperature Regulation In Animals
The bodies of animals have adapted to their environments.
For example, animals in colder habitats have a small surface area to volume ratios (S/V) to conserve maximum heat.
In hot areas, animals have a larger surface area to volume ratios to cool their bodies.
7. Digestion and Absorption Of Food
Chewed food has a greater surface area than unchewed food. This aids digestion as digestive juices like saliva can mix more thoroughly with it.
When the food reaches the stomach and intestines, they need to be absorbed.
Microvilli are tiny protruding structures on the lining of the small intestine. They increase the surface area through which digested food can be absorbed into the bloodstream.
8. Design Of Solar Panels
Solar panels are made with a huge surface area in order to maximize energy capture from the sun to generate electricity for home use.
The space station in space also has huge solar arrays that collect energy from sunlight.
Their surface area measures almost the size of a football field which gives enough capacity to power 40 homes.
There you have it; 8 real life examples of surface area. Surface areas are a very important property of solid objects. They determine how the objects interact with their environment and how we can use it in nature and technology.
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