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Surface Area and Volume - Maths

 

Different varieties of solid shapes are seen in our day-to-day life. It can be of any shape or size constructed from many different angles. Therefore, we can easily calculate both the surface area and volume of any object around us. Apart from this, it is also possible that many other objects could be of a combination of one or more objects. Thus, to calculate the surface area and volume of these new shapes and figures, we need to observe the shapes very well.

Firstly, the surface area is nothing but the total area of the surface that an object occupies. In other words, it can be described as the total area of all the surfaces of any given 3-dimensional or 2-dimensional figure. In terms of objects other than cuboid and cube, we should first calculate its lateral surface area and then add the surface area of its base. For cylinder and prism, we do the same, and then we take it as double the actual area of the base. Surface area is measured in square units.

An easy example to understand how exactly surface area works is given in the following statement. Imagine having an apple in our hand, and we decide to peel off its outer portion. So, as the apple is a 3-dimensional figure, and while we start to peel it off, we can notice that that red outer portion covers its entire body. So, this acts as the surface area for that apple.

The general form of the surface area is given below,

Surface Area = Lateral Area + (n * base)

Where,

n = number of bases present (n = 2 for cylinder / prism, n = 1 for cones / pyramids, n = 0 for circles/spheres).

Surface area can be further divided into two different types, such,

  1. Total Surface Area: It includes both the base and the curved part.
  2. Curved Surface Area: It only includes the curved part and not the base.

Volume

The volume of any object or figure can be easily understood by knowing how much amount of liquid a given 3-dimensional object can hold inside it. Volume is nothing but the quantity enclosed by the provided 3-dimensional object. The volume for one (lines) and two dimensional (squares) objects is zero as they don’t have a value on the 3rd axis to calculate it. Volume can only be calculated if an object contains three dimensions.

Following are some of the common properties of the volume of any object:

  1. To calculate the volume, an object should contain height, length and breadth. For example, volume = length * breadth * height.
  2. The total volume of any object is nothing but the sum of all enclosed regions.
  3. Every polyhedral region should contain a unique volume depending on the unit cube.

The following formulae are used in order to obtain volume for commonly used shapes:

Volume of Sphere (V) = 4/3πr³

Volume of Prism (V) = base area * height

Volume of Cone (V) = 1/3 * base area * height

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