[Maths Class Notes] on Length, Area and Volume Pdf for Exam

Length area and volume, Dimensional measures of one-dimensional, two- dimensional, and three-dimensional geometric objects. All three are magnitudes, that represent the “size” of an object. We can define length as the size of a line segment (see distance formulas), the area is the size of a closed region in a plane, and volume is the size of a solid. 

Formulas for the area as well as the volume are based on lengths. For example, the area of a circle equals π times the square of the length of its radius (denoted by r), and the volume of a rectangular box is the product of its three linear dimensions that is: length, width, as well as height.

In this article, we are going to discuss length area and volume, volume with fractional edge lengths and unit cubes, differential length area and volume as well as measuring volume as area times length.

What is Length?

Out of all the three-length area and volume. Length is a measure of distance. In the International System of Quantities, we can define length as a quantity with dimension distance. In most systems of measurement, a base unit for length is chosen, and from this base unit, all other various units are derived. In the International System of Units that is the SI system, the base unit for length is the metre (m).

Length is known to mean the most extended dimension of any given fixed object. However, this is not always the case, and the length of an object may depend on the position the object is in.

Various terms for the length of any given fixed object are used, and these include height, we can define height as the vertical length or vertical extent, and width, breadth, or depth. The term height is used when there is a base from which vertical measurements can be taken. The width or breadth of any object usually refers to a shorter dimension when the length is the longest one. Whereas depth is used for the third dimension of a three-dimensional object.

Let’s solve a problem!

Question 1. Bridge A is 50 m long, Bridge B is 24 m long. Find the total length of both the bridges.

Solution. Length of Bridge A = 50 m, Length of Bridge B = 24 m 

Total length of bridge A and B  = (50m + 24m) = 74 m 

What is Area?

Out of all the three-length area and volume. Area can be defined as the region bounded by the shape of an object. The space covered by any figure or any geometric shape is known to be the area of the shape. The area of all the shapes depends upon their dimensions as well as their properties. Different shapes have different areas. For example, the area of the square is different from the area of the kite.

If two objects are known to have a similar shape then it’s not necessary that the area covered by them will be equal unless and until the dimensions of both shapes are also equal.  Let’s suppose, there are two rectangle boxes, which have the length as L1 and L2 as well as breadth equal to B1 and B2. So the areas of both the rectangular box say, Area1 and Area2 will be equal only if L1 equals L2 and B1 equals B2.

 

Most Common Area Formulas 

 

What is Volume?

Out of all three – length area volume. We can define volume as a quantity that specifies the space occupied by a three-dimensional shape or object. The volume of a cube can be defined as the cube of its edge length (side3). For example, if the edge length of any given cube is equal to 5 cm, then its volume will be:

V = 5*5*5 cm equals 125 cubic cm

 

Unit of Volume

Out of length area and volume, the Volume of a solid is generally measured in cubic units. For example, if the dimensions are given in meters, then the volume of any object will be in cubic meters. Cubic meters are known to be the standard unit of volume in the International System of Units (that is SI). Similarly, various units of volume are cubic centimetres, cubic inches, cubic foot, etc.

 

Volume of Shapes