Definition of Length Area Volume
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.
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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
FAQs on Length, Area and Volume
1. What is the main difference between length, area, and volume?
The main difference lies in the number of dimensions they measure. Length is a one-dimensional measurement (like the length of a rope). Area is a two-dimensional measurement that tells you the surface covered by a flat shape (like a carpet on a floor). Volume is a three-dimensional measurement that tells you the space an object occupies (like the water in a bottle).
2. What are the simple formulas for calculating the area of a rectangle and the volume of a cuboid?
To find the area of a rectangle, you multiply its Length × Width. To find the volume of a cuboid (a box-like shape), you multiply its Length × Width × Height. This is often written as V = l × w × h.
3. If you know the volume of a box and two of its sides, how can you find the missing side?
You can find the missing side by dividing the total volume by the product of the two sides you already know. For example, to find the height, the formula would be: Height = Volume / (Length × Width). This method works for finding any single missing dimension.
4. How are length, area, and volume related to each other conceptually?
They build on each other in terms of dimensions. Length is a 1D measure. When you combine two length measurements (like length and width), you get area, which is a 2D concept. When you take that area and multiply it by a third length measurement (height), you get volume, which is a 3D concept. So, area is essentially length extended in a second direction, and volume is area extended in a third direction.
5. Why does a flat shape, like a square on paper, have an area but no volume?
A square on paper is a two-dimensional (2D) figure. It has length and width, which allows us to calculate its area. However, it has no third dimension—height or depth. Volume measures the space inside a three-dimensional (3D) object. Since a flat shape has no 'inside' space to fill, its volume is considered to be zero.
6. What are the common units used for measuring length, area, and volume?
The units change based on the dimension being measured:
- Length (1D): Measured in metres (m), centimetres (cm), or inches.
- Area (2D): Measured in square units, like square metres (m²) or square centimetres (cm²).
- Volume (3D): Measured in cubic units, like cubic metres (m³) or cubic centimetres (cm³). Litres (L) are also commonly used for liquid volume.
7. If you double the length of each side of a cube, what happens to its surface area and volume?
Doubling the sides has a much bigger effect on area and volume. The total surface area will become four times larger. The volume, however, will become eight times larger. This is because area scales by the square of the side length (2x2=4), while volume scales by the cube of the side length (2x2x2=8).
8. Can you give a real-world example of when you would need to measure length, area, and volume for the same project?
Imagine you are building a swimming pool. You would need to measure:
- Length: To determine the perimeter for fencing.
- Area: To calculate how many tiles are needed to cover the bottom surface.
- Volume: To figure out how much water is needed to fill the pool.
