Surface area and volume of 3-dimensional Figures
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Transcript of Surface area and volume of 3-dimensional Figures
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Surface area and volume of 3-dimensional Figures
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Cuboid
A Cuboid has 6 faces..
Each face is a rectangle.
Front
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faceface
face
Cube is also having 6 faces
( Here three faces are visible)
1
2 3
Dice (Pasa)
cube
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Surface area = Area of all six faces
= 6a2
a
Surface area
Cube cuboid
Surface area = Area of all six faces
= 2(lxb + bxh +hxl)
a
a
a
(Here all the faces are square) (Here all the faces are rectangular)
h
lb
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Area of base (Rectangle) = l x b
l
Height of cuboid = h
Volume of cuboid = Area of base x height = (l x b) x h
=lXbXh
h
Volume of cuboid
Front
b
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Volume of Cube
a
a
Area of base (square) = a2
Height of cube = a
Volume of cube = Area of base x height
= a2 x a = a3
a
a
a
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2πr
h
r
h
Curved Surface area of cylinder = Area of rectangle= 2πrh
Method of Finding Curved Surface area of Cylinder
r
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Total Surface Area of a Cylinder
=(2 π r) x( h) + 2 π r2
Curved surface
Area of curved surface + area of two circular surfaces
circular surfaces
= 2 π r( h+ r)
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Volume of cylinder
Volume of cylinder = Area of base x vertical height
= π r2 xh
r
h
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Curved Surface Area of Cone
Baser
h
l = Slant height
Curved Surface Area of a Cone = π r l where l = √ ( r²+h² )
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3( V ) = π r2h
r
h h
r
Volume of a Cone
Here the vertical height and radius of cylinder & cone are same.
3( volume of cone) = volume of cylinder
V = 1/3 π r2h
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If both cylinder and cone have same height and radius then volume of a cylinder is three
times the volume of a cone ,
Volume = 3V Volume =V
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4( 1/3πr2h ) = 4( 1/3πr3 ) = V
h=rr
Volume of a Sphere
Here the vertical height and radius of cone are same as radius of sphere.
4( volume of cone) = volume of Sphere
V = 4/3 π r3
r
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Surface area
6a2 2π rh π r l 4 π r2
Volume a3 π r2h 1/3π r2h 4/3 π r3
Comparison of Area and volume of different geometrical figures
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Circumference of circle = 2 π r
Area covered by cylinder = curved Surface area of of cylinder
= (2 π r) x( h)
r h
Method of finding Curved Surface area of cylinder
It is the area covered by the outer surface of a cylinder.
Formation of Cylinder by bangles
Circumference of circle = 2 π r
r