Volume vs Surface Area
Surface area and volume are two different but related concepts in mathematics and have great significance in construction as well as deciding the capacity of a room or a place. For example, if you are looking for a place to be your ware house, you obviously would like to know the volume of the place so that you can calculate how much product you can store easily. On the other hand, the concept of surface area is important as it decides the expenditure you need to incur when going in for painting the room (more the surface area, higher is the cost incurred on painting). Let us see the formula’s used to calculate the two important concepts and the difference and relation between volume and surface area.
Let us begin with the smallest and simplest of structures. How many match sticks a match box contains depends upon the surface area of the inside of the box as then you can easily calculate the number of matches that will fit in easily in the box. But the amount of water utilized by a single member of the family decides the the capacity of the water tank that you finally get installed at the rooftop. Here, it is volume and not surface area that you are concerned with. Volume of a rectangular room is the easiest to calculate as you need to multiply the area of the room with the height to get it. If the room is a square, it is all the easier as then one has to find the cube of the side of the room. One thing to remember for the student is that volume is always expressed in cubic units whereas area is expressed in square units. So, you have square feet or square meters as the surface area whereas the answer of volume is always in cubic feet or cubic meter. Surface area is always what we can touch while volume is what a body of given shape can contain.
You do not call it the area of the inside of an inflated balloon. You call it the volume of the balloon. So while volume is the space inside an object, area is the total area of the object. If we have a cube of a given side a, the area of each side is a X a, but there are 6 such sides, so the total surface area is 6 X a X a (= 6a²). The concept of surface area and volume is easily understood when we have to wrap a present after putting it into a box. The amount of gift paper that is consumed to wrap the box is dependent upon the surface area of the box, whereas the space inside the box reflects the volume of the box (or the present).
The surface area and volume are two concepts that have wide ranging application in real world, and are not meant to be wrapped inside text books only.
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In brief: Difference Between Volume and Surface Area • Surface area of a cool jug, if it is rectangular in shape, is its length X breadth, whereas its volume is known when the height of the cool jug is also taken into consideration • Surface area is two dimensional whereas volume is three dimensional • Units of surface area are square feet or square meters whereas units of volume are cubic feet or cubic meter. • You have to take into consideration surface area of the walls of a room when you are getting it painted, whereas you need to calculate its volume if you want to know the capacity of the room if it is to be used as a warehouse.
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