Measurement; Time, Regular and Irregular Objects, Area and Volume

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Overview

The interval between any two events is called time and the total space occupied by a body is called its volume. This note provides information about time, area, and volume.

Measurement; Time, Regular and Irregular Objects, Area and Volume

Time

Source: www.jimdirectory.com Fig: Clock
Source: www.jimdirectory.com
Fig: Clock

The duration between any two events is called time. The SI unit of time is second.

Measurement of Time

For the measurement of time, a clock is used. There are different types of clocks like the mechanical clock, wristwatch, pendulum clock, quartz clock, etc. Time is measured in different ways. It can be measured in second, minute, hour, day, week, month, year etc. Second is the smallest unit of time. For the short time period, we use second, minute and hour and for log time period, we use day, week, month and year. For the measurement of the very long time period, we use decade, century, millennium, etc. The multiples and sub- multiples of a second are given below,

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60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
365 days = 1 year
10 years = 1 decade
100 years = 1 century
1000 years = 1 millennium

Regular and irregular objects

Various types of substances are found in our surrounding. They have different shape and sizes. Some substances have fixed geometrical shape and some do not have. Those substances that have fixed geometrical shapes are called regular objects. Some of the examples of regular objects are books, pencils, chalk box, basketball, etc.
Those substances which do not have a fixed geometrical shape are called irregular objects. Some of the examples of irregular objects are the pieces of broken glass, a piece of stone, a broken piece of brick, leaf, etc.

 

Area

The total space occupied by the plane surface of the object is known as the area of that object. The SI unit of area is the square metre (m2). Other similar units of area are mm2, cm2, km2, etc.

Measurement of Area of Regular Plane Surfaces

There are various formulae used for the measurement of the area of the regularplane surface. Some of them are given below,

  • Area of a rectangular object (A) = length(l) \(\times\) breadth(b)
    \(\therefore\) A= l \(\times\) b
  • Area of a circle (A)=π \(\times\) (radius)2[ π = \(\frac{22}{7}\) ]
    \(\therefore\) A=πr2
  • Area of a square (A)= (length)2
    \(\therefore\) A= l2

Example 1
The radius of the circle is 7cm, if the value ofπ is \(\frac{22}{7}\), then what is the area of circle.

Solution:
Given,
Radius (r)= 7 cm
π = \(\frac{22}{7}\)
Area (A)= ?
By using formula,
A =πr2
=\(\frac{22}{7}\) \(\times\) 72
= 22 \(\times\) 7
= 154cm2

Measurement of Area of Irregular Surfaces

There are no exact formulae for the measurement of the area of irregular surfaces. But we can measure the area of irregular surfaces by using graph paper. A graph paper is divided into equal- sized squares of side 1 cm and 1 mm.
At first, the irregular object is placed on the graph paper. Then the outline of the object is drawn on the graph paper. After this, the number of squares covered by the outline is counted. The number of squares that are more than half is also counted but the squares less than half are not counted. Then by adding two numbers, the area of the given irregular object is calculated.

 

Volume

The total space occupied by the body is called volume. In SI system, the unit of volume is a cubic meter (m3). Other similar units are mm3, cm3, ml, l, etc. The volume of solid is measured in mm3, cm3, m3, etc. Measuring cylinders are used for the measurement of the volume of liquids. The volume of liquids is measured in ml, l, etc,

1 ml = 1cm3 or 1cc (cubic centimetre)
1000 ml = 1l (litre)
1000 cm= 1l

Measurement of Volume of Regular Solids

For the calculation of the volume of regular solids, various formula is used which are given below,

  • Volume of a cuboid (V)= length(l) \(\times\) breadth (b) \(\times\) height(h)
    \(\therefore\) V= l \(\times\) b \(\times\) h \(\times\)

  • Volume of a cube (V)= (length)3
    \(\therefore\) V= l3
  • Volume of sphere (V)= \(\frac{4}{3}\)π(radius)3
    \(\therefore\) V=\(\frac{4}{3}\)πr3
  • Volume of cylinder (V)=π \(\times\) (radius)2 \(\times\) height (h)
    \(\therefore\) V=πr2h
    Source: geometryworld.blogspot.com Fig: Cuboid, Cube, Sphere, Cylinder
    Source: geometryworld.blogspot.com
    Fig: Cuboid, Cube, Sphere, Cylinder

Example 2

The length, breadth and height of the cuboid is 3cm, 6cm and 9cm respectively. Calculate the volume of cuboid.

Solutions:
Given,
Length(l)= 3cm
Breadth(b)= 6cm
Height(h)= 9cm

According to the formula, we have

\(\therefore\) V= l \(\times\) b \(\times\) h \(\times\)
= 3 \(\times\) 6 \(\times\) 9
= 162cm3

Measuring the Volume of Liquids

Source:www.dorthonion.com Fig: Water and Mercury
Source:www.dorthonion.com
Fig: Water and Mercury

The volume of the liquids are measured by using differnt measuring cylinders such as graduated cylinder, milkman's measure, pipette, burette, milkman's measure. etc. It is measured in millilitre(ml) or cubic centimetre (cc) and litre(l). Litre is mostly used.
At first for the measurement of the volume of liquids, the liquid is poured into the measuring cylinder, then the volume of the liquid is calculated by observing the reading given on the surface of the cylinder.
There are various types of liquids. While measuring the volume of liquids, some liquids form a concave surface on the cylinder and some form convex surface in the cylinder. Liquids like oil, water, alcohol, etc form a concave surface and liquids like mercury, etc form a convex surface in the cylinder. For the liquid forming convex surface, the reading should be taken from the upper meniscus and for the liquid forming concave mirror, the reading should be taken from the lower meniscus.

Measuring the Volume of Irregular Solids

We can measure the area of irregular bodies by using graph paper. But it is impossible to measure the volume of irregular bodies by using graph paper. We can measure the volume of irregular bodies by using measuring cylinder. This method is based on the fact that the volume of an irregular solid is equal to the volume of water displaced by it when it is immersed in water. When we immerse an irregular body in water, it displaces some amount of water. The volume of displaced water is equal to the volume of an irregular body that displace water. This method can be used to calculate the volume of those irregular bodies which sink in water and do not dissolve in water.

Experiment 1
Object: To measure the volume of a piece of stone.
Materials Required: Measuring cylinder, water, thread, a piece of brick

Procedure

Af first, fill the measuring cylinder partially with water. Note down the level of the water. Let it be the initial level of water, V1. While recording the level of water, keep the eye in the level with the bottom of the meniscus to avoid parallax error. After this, tie the piece of stone with the help of thread and immerse it into the water of measuring cylinder. We can see that, the level of water rises. Then, note down the new level of water carefully. Let it be the final reading, V2.

Source: gmscience.wordpress.com Fig: Measuring volume of a piece of stone
Source: gmscience.wordpress.com
Fig: Measuring volume of a piece of stone

Observation

Suppose V1 is 50 ml and V2 is 75 ml.
Now,
Initial volume of water in the cylinder (V1)= 50 ml
Final volume of water in the cylinder (V2)= 75 ml
\(\therefore\) Volume of the water displaced (V)=V2 -V1
= 75ml - 50ml
= 25ml

\(\therefore\) Volume of the Stone= Volume of water displaced
= 25ml

Precautions

  • While taking the readings, the water should be at rest and the measuring cylinder should be placed on a horizontal surface .
  • For the liquid forming convex surface, the reading should be taken from the upper meniscus and for the liquid forming concave mirror, the reading should be taken from the lower meniscus.

 

Things to remember
  • The interval between any two events is called time.
  • The SI unit of time is second.
  • Those substances which have fixed geometrical shape are called regular objects.
  • Those substances which do not have a fixed geometrical shape are called irregular objects.
  • The total space occupied by the plane surface of the object is called area.
  • The SI unit of area is a square metre (m2).
  • The total space occupied by an object is called the volume of that object.
  • The volume of liquids can be measured by measuring cylinders.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Measurement; Time, Regular and Irregular Objects, Area and Volume
Measurement of Time
Measurement of Volume
Measurement of volume of irregular solids
Measuring volume of liquids
Questions and Answers

Solutions:
Given,
Length(l)= 9cm
Breadth(b)= 5cm
Area(A)= ?

By using formula we have,

A= l \(\times\) b
    = 9 \(\times\) 5
    =45cm2

\(\therefore) The area of the rectangular brick is 45 cm2.

Solutions:
Given,
Radius (r)= 9cm
Volume (V) = ?

By using formula, we have

V= \(\frac{4}{3}\)πr3 [Since football is a sphere]
    = \(\frac{4}{3}\) \(\times\) \(\frac{22}{7}\) \(\times\)9 \(\times\) 9 \(\times\) 9
    = 3052.08 cm3

\(\therefore\) The volume of football is 3052.08 cm3.

Solutions:
Given,

Length(l)= ?
Volume(v)= 27 cm3

According to the formula, 

Volume of cube(v)= (Length)3
                     
Or, V= l3
                  Or, 27= l3
                     
Or, 33= l3
                  Or, l = 3cm

∴ The length of the cube is 3 cm.

  • Time: The interval between any two events is called time.
  • Regular objects: Those substances which have fixed geometrical shape are called regular objects.
  • Area: The total space occupied by the plane surface of the object is called area.
  • Volume: The total space occupied by an object is called volume of that object. 
  • Area of a rectangular object (A) = length(l) \(\times\) breadth(b)
    \(\therefore\) A= l \(\times\) b
  • Area of a circle (A)=π \(\times\) (radius)2[ π = \(\frac{22}{7}\) ]
    \(\therefore\) A=πr2
  • Area of a square (A)= (length)2
    \(\therefore\) A= l2
The interval between any two events is called time.
Those things which have a fixed geometrical shape are called regulr objects.
Those things which donot have a fixed geometrical shape are called irregulr objects.
The SI unit of area is square metre.
The total space occupiedby an object is called volume.
The SI unit of Volume is cubic metre.
Second is the smallest unit of time.
Area is the total space occupied by the plane surface of the object.
The SI unit of time is Seconds.
The shopkeepers use an ordinary grocer's balance to measure he mass of vegetables.
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