Area Opf Plane Figures_dakhab

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Vii Manjinder Singh Jaspreet Singh Sham Singh Navtejpal singh

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We from the core of our hearts sincerely thanks to our subject teacher Mrs.Inderjit Kaur and our guidance teacher Mr. Sukhwinder Singh and also to our seniors for their kindness and help.

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1.Surface areas and volumes 2 Cuboid And Cube 3 Surface Area 4 Volume 5 Examples

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Introducation Some figures that are not plane figures these figures are Cuboids and Cubes. These figures do not lie in a plane. Such figures are called Solid (three dimensional) figures.

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A cuboid is made up of six rectangular regions. Each region is called a face of the cuboid. A cuboid has six faces. There are three pairs of congruent opposite faces in a cuboid.

FIG NO-1 In Fig-1. ABCD is the top face and EFGH is the bottom face(or base).ABFE is the front face and CDHG is the back

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face while BFGC and AEHD are the side faces. The faces other than the bottom and top are called lateral faces also. In cuboid, we find eight corners. Each of these is called a vertex of the cuboid. In Fig. A,B,C,D,E,F,G and H are the vertices of the cuboid. Three distinct lengths longest of these is called the length of the cuboid and out of remaining two, one is called the breadth(or width)and the other the height (or depth or thickness) of the cuboid. For Example: A Chalk Box, A Classroom, A Cardboard box.

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FIG NO-2 The length, breadth and height of a cuboid are usually denoted by the letter symbos l, b and h respectively. A cuboid whose length ,breadth and height are equal is called a cube.

Surfce of a cuboid consists of six rectangular faces The sum of the areas of these six rectangular faces is called the total surface area of the cuboid.

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FIG NO-3 Let the length, breadth and height(in cm)of a cuboid be l,b and h respectively. Then, area of bottom(base)and top faces =(l × b + l × b)cm2 =2lb cm2 Area of side faces =(b×h+b×h)cm2 =2bh cm2 And area of front and back faces =(h × l + h × l )cm2 =2hl cm2 Total surface area=(2lb+2bh+2hl ) cm2

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=(lb+bh+hl)cm2 The lateral surface area of the cuboid=2(lh + bh) square units =2(l + b)h square units =perimeter of the base × height In the case of a cube,l=b=h. Surface area of a cube of side l units =2(l×l+l×l+l×l) square units =6 l2 square units

The space occupied by a solid(in fact solid region)is called its volume.A rectangular tin box is to be made to store oil.The greater the volume of the cuboidal region,the more is the quantity of oil it can store.

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V=l×b×h V is the volume of the cuboid(in cm).if l,b and h are in cm. In the case of a cube, l=b=h, therefore, Volume of a cube=L×L×L=L3 cubic units Example: find the volume of a block of Wood whose length, breadth and Height are respectively 10cm,5cm and 3cm. Solution: v=l × b × h V=10×5×3cm3=150cm3

Example: find the volume of a cube whose edge is 8m. Solution: volume = L3 = 8×8×8m3

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=512m3