The measurement is an entity through which we can know about the size or value or count or length of an object. It is an important thing which we use it daily in our lives. We can measure an object using any instrument in early age early man was used to use his body parts for measuring purpose.Measurement of object can be done in different ways:
Based on their construction of geometrical figure.
Based on rotation of the earth,motion of the moon and planets and oscillation within atoms.
By measuring the length of figure with scale.etc
Measures of 3-dimensional Figures
Based on their construction of geometrical figure
Depending on the construction of the geometrical figure we can measure the angle,sides, axis etc and can easily measure the figure and can give its propeties and type of the figure etc. This is the easy method and best method which we use ina analysis of geometrical figures.
Example:
Here in the above figure the angle is 90 degrees so its right angle trianngle,with two equal sides.
Based on rotation of the earth,motion of the moon and planets and oscillation within atoms
The exact length of time for the earth to rotate around the sun is 365 days 5 hours 48 minutes and 46 seconds
In early times various body parts were used as tools and guides, hence the word "feet," or "the rule of thumb," or “pulse”.
The term, "taxicab", was formed from combining the word, taximeter and cabriolet. Taximeter is a tool for measuring time and distance and a cabriolet is a 2 wheeled 1 horse carriage.
The term "horsepower", is the unit of energy needed to lift 550lbs 1ft. in the air for 1 second by an average strength horse.
By measuring the length of figure with scale
Depending on the scale we can measure the length of the sides.
Different geomtrical figures having different way of measuremnet based on the criteria of requirement ie like volume, area, radius etc.
Pythagorean Theorem
Pythagorean Theorem, which states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides.Median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal parts.
Formulas for Measurements
Areas of some geometric shapes
Square:
A=S2
Where:
S= length of side.
Rectangle:
A= L x B
Where:
L=length of a rectangle
B=breath of a rectangle
Parallelogram:
A=B x H
Where:
B=Breath of a parallelogram
H=Height of a parallelogram
Trapezoid:
A=h/2(b1+b2)
Where:
h=height of a trapezoid
b1,b2=breaths
Circle:
A= piXr2
Where:
Pi=3.14 (constant value)
r=radius
Volume formulas
Cube:
V=a3
Where:
A=length of the side
Cuboids:
V=a x b x c
Where:
A,b,c are lengths of the sides.
Cylinder:
V= pi r2 h
Where:
pi = 3.14(constant value)
r=radius
h=height
Pyramid:
V=1/3 b h
Where:
B=breath
H=height
Cone:
V= 1/3 pi r2 h
Where
pi = 3.14(constant value)
r=radius
h=height
Sphere:
V=4/3 pi r3
pi = 3.14(constant value)
r=radius
In the above formulas we always use a common entity length to find them out and their units are always defined in lengths.
Proportions to Convert to Equivalent Measurements
Two quantities are said to be proportional if they vary in such a way that one quantities is a constant multiple of the other, or equivalently if they have a constant ratio.Proportionality obtains when two ratios are equal. It is therefore defined as the equality between two ratios.
Its denoted by symbol "?" is used to indicate that two values are proportional.
The ratio between 3:9 and 1:3 is equal so the are proportional to each other. This can be written as.
3:9=1:3 (or) 3/9=1/3
Properties:
The proportionality obtains only when two ratios are equal.
It also obtain when two ratio's are reciprocal(inverse).
The change in one quantity affects the other quantity vice versa.
Types
They are two types of proportions:
?Direct proportion
Direct proportion:
If the change in one quantity directly affects the other quantity then that is known as direct proportion. In direct proportion we can only have two quantities the change in one affects the other directly.
Consider two quantities x and y ; if they are in direct proportion then what ever changes occur in X will affect Y directly.
They are represented as below:
X ? Y
Where,
?- represents the direct proportionality.
The direct proportional changes when we introduce constant k in between i.e. X are made equal to Y by multiplying Y with constants K
X=kY
Where
k- is a universal constant.
Inverse proportion:
Inversely proportion is the proportionality that decreases one quantity when another quantity is increased or increases one quantity when another quantity is decreased. It is opposite to direct proportionality. Two quantities are said to be inverse when one quantity is directly proportion to the reciprocal of other.
If two quantities X and Y are inversely proportion then they are generally represented as:
X ? 1/Y (or) X ? Y-1
And these two quantities are equivalent when a constant k is introduced. And it is written as.
X=k (1/Y) (or) X=k/Y
Where,
k=universal constant.
Here X and Y are inversely proportion if when X changes then Y changes reciprocally to X.
Scale Drawings
A scale is a model which is used to design a pattern for number system,it is shown as length in drawing.A scale model is a representation or copy of an object that is larger or smaller than the actual size of the object,usually scale model is smaller than the original size of an object.
Scale drawings are based on the geometric principles.Using these scale drawings we can find out the similarities and difference between any geometric figures.Scale drawings are very important for architects, builders, carpenters, plumbers etc,because they are majorly used for designing purpose.
Example:
Represent the scale from -3 to +3?
Given: Representing scale -3 to +3
Properties
They are used for designing geometrical figures.
Comparison between any two figures can be done using this models.
These scales are used to locate the points in the co-ordinate system.
They are used to solve problems(co-ordinate system,geometry).
Mapping is one of the major property in scale drawing.
Types
Accurate scale drawing
Detailed scale drawing
Accurate scale drawing:
Accurate scale drawing are the rough drawing which contains all the ideas of the models.In this model the scale representation will be accurate ie in digits.
Detailed scale drawing:
Detailed scale drawing is the structure of the given model,which is obtained after mapping all the ideas together.
In this drawing we will get detailed structure about the model.
Scales Based on Graphs
A numerical value is generally used for scaling purposes i.e. to find out the range, value ,mean and count of a particular object. The numerical value is represented by a key word called number.Depending on values we can represent data in statistical tables and can give ranks to the data ,we can even find frequency distribution.
Pie-chart:
Pie chart is represented in a circle. Therefore its also known as "circle graph". The circle is divided into different partition depending on Category. It is one of the most common graphs for describing a set of measurements. It is the best graphical display for displaying data arranged in categories. Each category is represented by a wedge of the pie and the size of each wedge is in proportion to the percentage of each category.Therefore we can represent data in different category based on the data provided.
Bar graph:
A bar graph consist two axes and a series of horizontal bars or vertical bars are placed in the x ,y plane,depending on the value. It’s another way of displaying qualitative data.The frequencies along the vertical axis (ordinate) of the chart and the categories on the horizontal axis of the chart (abscissa). Bar chart is used to display frequency and percentages.
Related Tags
3-Dimensional Figures measurement , how to measure 3-Dimensional Figures