In my daily life, I have no use for the surface area and or volume of a cube. None whatsoever.
Surface area: when you want to paper a room or pain it. Volume: When you want to know how much stuff you can cram into the boot of your car, or in a fridge, suitcase.
They are important concepts in math and phsyics. Surface area of a room for example tells us how much paint we need. Volume of a fish tank tells us how much water to put in. There are millions of every day applications for both these conceps in every day life and that is why there are so important.
Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.
If you want to paint a place, carpet it, plant wheat on it, water it, mow it, pave it, or cover it with cloth, then you need to know what its surface area is. If you want to fill a place with water or beer, or pretty much fill any container with anything, then you need to know what its volume is.
Surface area is important for the exchange of materials, such as nutrients and waste products, with the environment, while volume determines the cell's metabolic activity and energy requirements. Cells need a high surface area-to-volume ratio to efficiently perform these functions and maintain homeostasis. If a cell becomes too large, its surface area-to-volume ratio decreases, making it difficult to meet its metabolic needs.
Surface area, is used to paint a house or wrap a present and volume is used when you need to know how much water to put in your fish tank or water bowl
The larger the volume of a cell the harder it is to transfer objects, such as food, to the other side. If a cell could keep growing it would no longer be able to support it's own life.
This is because of the surface area compared to the volume area Eg. A small size : large surface area to a small volume. Or the movement of required particles would take to long to sustain life if the cell is to big.
Surface area in mammalian anatomy can be as simple as a change in body size in subspecies from one climate to another. Larger animals have an easier time conserving heat and smaller ones (those with large surface area to volume) are better at releasing heat. Elephants with large ears can dissipate heat better than those with smaller ears for example. Increased surface area to volume increases the rate of infiltration of nutrients into a complex living system. Many small cells require less energy and have a larger surface area to volume so nutrients can be absorbed faster and utilized more rapidly. Waste products can be excreted more quickly as well. Increased surface area in lungs (alveoli), intestines (villi), reticulated endothellium, and Golgi apparatus facilitate rapid absorption, and production of cellar components necessary for life as well as expiration of wastes. The list is much longer than this...
It depends on what you want to measure: You could want to know: the area, the depth, the volume of water, surface temperature, temperature at depth, salinity, pollution level, animal life, etc
For example, many liquids are sold by volume (such as, "please sell me a liter of milk").