Current Affairs 5th Class

  Introduction     You might have seen in the books, newspaper, etc. graphs are used to give somevaluable information, like people living under poverty line in different states, numberof malnutrition child in different Asian countries, number of unemployed peoplein India, number of uneducated people in a particular state, etc. To prepare graphinformation?s, observations are made. These observations are written in the numeralform, called data. Further data is arranged in many ways in order to easily extractthe information contained by it. In this chapter we will study about the data andanalysis of data with the help of graph.  

   Volume   In our daily life the number of things is stored in different kinds of container. Holding capacity of a container is called its volume. For ex.: The amount of water that a bucket can hold is called volume of the bucket.         Volume of the Cuboid Volume of a cuboid = Length \[\times \] breadth \[\times \]height =lbh.     In the cuboid ABCDEFG Length of the cuboid = AB Breadth of the cuboid = AE Height of the cuboid = BC Thus volume of the cuboid \[\text{ABCDEFG=AB }\!\!\times\!\!\text{ AE }\!\!\times\!\!\text{ BC=6 }\!\!\times\!\!\text{ 5 }\!\!\times\!\!\text{ 5=150 c}{{\text{m}}^{\text{2}}}\text{.}\]       Find the volume of the following cuboid:     Explanation In the cuboid PQRSTUV Length of the cuboid = PQ = 7 cm Breadth of the cuboid = PT = 5 cm Height of the cuboid = PS = 6 cm Thus volume of the cuboid PQRSTUV \[\text{=PQ }\!\!\times\!\!\text{ PT }\!\!\times\!\!\text{ PS}\] \[=\text{ }7\text{ }cm\times 5\text{ }cm\times 6\text{ }cm\text{ }=210\text{ }c{{m}^{3}}.\]       Volume of a Cube Volume of a cube \[\text{= sid}{{\text{e}}^{\text{3}}}\text{.}\]     In the cube ABCDEFG Volume of the cube ABCDEFG \[\text{A}{{\text{B}}^{\text{3}}}\text{=(8CM}{{\text{)}}^{\text{3}}}\text{=512C}{{\text{M}}^{\text{3}}}\]       Find the volume of the following figure:     Solution: In the cube ABCDEFG Volume of the cube ABCDEFG \[\text{=AB(6}\,\text{CM}{{\text{)}}^{\text{3}}}\text{=216}\,\text{c}{{\text{m}}^{\text{3}}}\]      

• If base of triangle is doubled, the area of the triangle also gets doubled.
• If area and perimeters of a circle are numerically equal, numeric value of the radius of the circle is 2.  

   

• Perimeter is defined as the length the length of boundary line of a close geometrical figure.
• Perimeter of a triangle is defined as the sum of all three sides.
• Perimeter of an equilateral triangle is given by 3 \[\times \] length of a side.
• Perimeter of a rectangle is given by 2 (length + breadth).
• Perimeter of a square is given by 4\[\times \] side.
• Space occupied by an object is called area.
• Area of square is given by \[\text{sid}{{\text{e}}^{\text{2}}}\text{.}\]
• Holding capacity of a container is called volume.

            Length of one side of an equilateral triangle is 4.3 cm. Find the perimeter of the triangle. (a) 12.3cm                                           (b) 12.6cm (c) 12.9cm                                           (d) 12.12cm                        (e) None of these   Answer: (c)                 Explanation All three sides of an equilateral triangle are equal. Therefore, more...

  Area   All the geometrical shapes occupies some space. The occupied space by a geometrical shape is called area of that geometrical shape.                           Shaded part in the above figures represent area.         Area of a Triangle Area of a triangle \[=\frac{1}{2}\times \] base x height.     Height In a triangle, the length of the perpendicular which is drawn from vertex to the opposite side is called height of the triangle.   Base  In a triangle, the length of the side of the triangle on which perpendicular is drown is called base.     Area of a triangle \[=\frac{1}{2}\times \] base \[\times \] height In triangle ABC Height = CD and base = AB Area of the triangle \[ABC=\times AB\times CD.\]       Find the area of the following figure:     Explanation Area of a triangle \[=\frac{1}{2}\times \] base \[\times \]height In triangle PQR Area of the triangle \[\text{PQR=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ QR }\!\!\times\!\!\text{ PS=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 4cm }\!\!\times\!\!\text{ 7cm14c}{{\text{m}}^{\text{2}}}\]       Area of a Rectangle Area of a rectangle = length \[\times \] breadth.       Length The longer side of a rectangle is called length of the rectangle.       Breadth The shorter side of a rectangle is called breadth of the rectangle.     In the rectangle PQRS Length of rectangle = Longer side PQ = RS = 7 cm Breadth of the rectangle = Shorter side QR = SP = 5 cm Area of the rectangle PQRS = Length \[\times \] Breadth = PQ \[\times \] QR.       Find the area of the following figure:     In rectangle ABCD Length = AB = 6 cm Breadth = BC = 4 cm Thus area of the rectangle 3 \[\text{ABCD=AB }\!\!\times\!\!\text{ BC=6 cm }\!\!\times\!\!\text{ 4 cm=24 c}{{\text{m}}^{\text{2}}}\text{.}\]       Area of a Square Area of a square\[~=\text{ }sid{{e}^{2}}.\]     In the square PQRS PQ=QR=RS=SP Area of the square \[PQRS\text{ }=\text{ }PQ\text{ }\times \text{ }PQ\] \[=P{{Q}^{2}}.\]       Find the area of the following figure:     In square ABCD AB = BC = CD = DA = 5 cm Area of the square \[\text{ABCD more...

   Perimeter     As we know all the geometrical shapes like triangles, quadrilaterals, etc. occupy some area. Perimeter is referred as the length of the boundary line which surrounds the area occupied by a geometrical shape. In the rectilinear figures the line segment which bounds the area are called sides. Thus we can say perimeter of a geometrical shape is the sum of the length of the all sides which bound the area occupied by that shape.       Find the perimeter of the following figure:     Explanation Perimetre of the figure \[=AB+BC+CD+DE+EA\] Perimetre of the figure \[=4.5cm+4cm+2.5cm+3cm+4cm=18cm.\]       Perimeter of the Triangles A triangles has three sides.     Perimetre of the triangle \[\text{ABC=AB+BC+CA}\] Thus, perimetre of a triangle is the sum of length of its three sides.       Find the perimetre of the following triangle:   Perimetre of the triangle \[~ABC=AB+BC+AC\] \[=4\text{ }cm+3.5\text{ }cm+5cm\] \[=12.5\text{ }cm.\]       Perimetre of an Equilateral Triangle Perimetre of an equilateral triangle is equal to \[3\times \]side.     Perimetre of the triangle \[~ABC=AB+BC+CA\]                 In an equilateral triangle all sides are equal Therefore,\[~AB=BC=CA\] Thus perimetre of the equilateral triangle \[ABC=AB+AB+AB\] \[=3\times AB\] AB is a side of the equilateral triangle ABC. Therefore, perimetre of an equilateral triangle \[=3\times \]side.       Find the perimetre of the following triangle:                     Explanation Perimetre of an equilateral triangle \[=3\times \]side In the triangle ABC Perimetre of the triangle\[~ABC=3\times AB\] \[\therefore AB=BC=CA=4cm\] Therefore, perimetre of the triangle ABC \[=3\times 4\,cm\] =12 cm.       Perimetre of Isosceles Triangle     Perimetre of the triangle \[XYZ=XY+YZ+ZX\] An isosceles triangle has two equal sides In the triangle \[XYZ,\] \[XY=XZ\] Thus perimetre of\[~XYZ=XY+XY+ZX\] \[=2\times XY+YZ\] Here \[XY\] is one of the equal sides. Therefore, perimetre of an isosceles triangle \[=2\times \]length of one of the equalsides + length of the unequal side.       Find the perimetre of the following triangle:   Explanation Perimetre of an isosceles triangle \[=2\times \]one of the equal sides + unequal side In the triangle \[XYZ\] .             Perimetre of the triangle \[XYZ\text{ }=2\times XY+YZ\] \[XY=ZX=3\text{ }cm\]and\[YZ=4cm\] therefore, perimetre of the triangle \[~XYZ=2\times 3\text{ }cm+4\text{ }cm\] \[=10\text{ }cm.\]       Perimetre of Scalene Triangles   more...

   Introduction     In our daily life we see a variety of articles of different shapes and sizes. We require to know what space a particular article occupies, what is its capacity, how much substance requires to make that article, etc. In this chapter we will study perimeters, areas, and volumes of different geometrical shapes.  

  Quadrilateral     The geometrical figure having four sides is called quadrilateral.     Properties of Quadrilateral A quadrilateral has: (i) Four sides (ii) Four angles (iii) Four vertices     Sides of the quadrilateral ABCD are AB, BC, CD, and AD. Angles of the quadrilateral are ZABC, ZBCD, \[\angle CDA,\]and \[\angle DAB.\] Vertices of the quadrilateral ABCD are point A, point B, point C and point D.       Types of Quadrilateral In this chapter we will study about two types of quadrilateral (i) Rectangle (ii) Square     Rectangle Rectangle is a quadrilateral in which (i) All angles are of 90° (ii) Opposite sides are equal.     ABCD is a rectangle in which (i)\[\angle A=\angle B=\angle C=\angle D={{90}^{o}}\] (ii) AB=CD=7 cm, and BC=AD=5cm.       Square Square is a quadrilateral in which (i) All angles are of \[{{90}^{o}}\] (ii) All sides are equal.     ABCD is a square in which (i)\[\angle A=\angle B=\angle C=\angle D={{90}^{o}}\] (ii) AB = BC = CD = DA = 6 cm.                                                                            Circle Circle is a close curved line whose all points are at the same distance from a given point in a plane.       Centre of a Circle The point from which all the points of the curved line are at the same distance is called centre of the circle.     In the given figure, 0 is the centre of the circle.       Radius of a Circle Distance between the centre and the curved line of a circle is called radius of the circle.     In the given figure, OA is the radius of the circle                 Note: All the radius of a circle are equal in length       Chord of the circle Any line segment which joins the two points of the curved line of a circle is called chord of the circle.     In the figure, AB is the chord of the circle       Diameter of the Circle The longest chord of a circle is called diametre of the circle. In oth8er word the chord which passes through the centre is called diametre of the circle.   In the figure, AB more...

     Angle     Inclination between two rays having common end point is called angle.     In the above given picture, OA and OB are two rays which have a common end point 0. Point 0 is called vertex and rays OA and OB are called arms. The inclination between the rays OA and OB is called angle AOB, and it is denoted as \[\angle \text{AOB}\text{.}\]     Angle is measured in degree. Symbol of the degree is \[~{{''}^{o}}''\] and written as \[{{a}^{o}}.\]         Types of Angle      There are different types of angles. (a) Acute angle                    (b) Right Angle (c) Obtuse angle                   (d) Straight angle     Acute Angle An angle which measures between 0° and 90° is called acute angle.       Measure the given below angle and find is it an acute angle.                   Explanation                 Measure of the above given angle is \[{{40}^{o}}.\] Therefore, the angle is an acute angle     Right Angle An angle of \[{{90}^{o}}\] is called right angle.         Obtuse Angle An angle which measures between \[{{90}^{o}}\] and \[{{180}^{o}}\] is called obtuse angle.       Straight Angle                 An angle which measures \[{{180}^{o}}\] is called straight angle.           Triangle The geometrical shapes having three sides are called triangle.         Properties of Triangle Triangle has: (i) Three sides,                                  (ii) Three angles                                      (iii) Three vertices     Three sides of the triangle \[\text{XYZ}\]are\[\text{ }\!\!~\!\!\text{ XY, YZ,}\] and \[\text{ZX}\] Three angles of the triangle are \[\angle \text{X,}\angle \text{Y,}\]and \[\angle Z\] Three vertices of the triangle are point \[\text{X,}\] point Y, and point Z.       Types of Triangle Triangle has been classified: (a) On the basis of sides (b) On the basis of angles       Sides Based Classification On the basis of sides, triangles are of three types (i) Equilateral Triangle (ii) Isosceles Triangle (iii) Scalene Triangle       Equilateral Triangle A triangle whose all sides are of equal length is called equilateral triangle.   \[\Delta \] ABC is an equilateral triangle as AB = BC more...

  Point and Line Segment       Point To show a particular location, a dot (.) is placed over it, that dot is known as point Ex:   ln the above given picture Point A shows Aleena, point B shows Jack, point C shows James' Point D shows Kristy, point E shows Janey and point F shows Rocky.         Which one of the following figures contains the symbol of point?     Solution:  The fourth figure contains the symbol of point (.)                     Line Segment Line segment is defined as the shortest distance between two fixed points Ex: It is denoted as ab.       Features of a Line Segment A line segment begins from a fixed point and ends at a fixed point. Therefore, its length can be measured. The first and the last point of a line segment are called the end points. A line segment has two end points.       How many line segments are there in the figure?         Solution: There are 5 line segments are there in the figure \[\underline{\text{AB}}\text{,}\underline{\text{BC}}\text{,}\underline{\text{CD}}\text{,}\underline{\text{DA}}\text{,}\]and\[\underline{\text{AC}}\]       Ray It is defined as the extension of a line segment in one direction up to infinity. Ex:       It is denoted as \[\overrightarrow{\text{AB}\text{.}}\]                        Features of a Ray A ray begins from a fixed point and goes up to infinite. Therefore, only its beginning point can be identified. A ray has only one end point and its length can not be measured.     How many rays are there in the given figure? Name them.       Explanation There are eleven rays in the figure.                 \[\]Line is defined as the extension of a line segment up to infinity in either direction.     It is denoted as \[\]         Features of a Line A line has no end point as it goes to infinity in either direction, therefore, neither its beginning point nor last point can be identified. That is why its length cannot be measured.           How many lines are there in the following figure?     There is only more...

   Introduction     We observe different types of figures around us. Look at the following pictures:                                      (a) Railway track                               (b) Electric pole                                              (c) Triangular park                              (d) Pentagonal park   (e)  Coin   In the above given pictures we see that they are in different shapes. In this chapter we will discuss about different types of geometrical figures such as line, angles etc.