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Surface area and volume of different Geometrical Figures
Cube CuboidCylinder Cone
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faceface
face
Total faces = 6 ( Here three faces are visible)
1
2 3
Dice
Faces of cube
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Faces of a Cuboid
Brick
Book
Face
Face
Face
Total faces = 6 ( Here only three faces are visible.)
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Cores
Total edges = 12 ( Here only 9 edges are visible)
Edges
Note Same is in the case in Cuboid
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Surface area = Area of all six faces
= 6a2
ab
Surface areaCube Cuboid
Surface area = Area of all six faces
= 2(axb + bxc +cxa)
c
a
a
a
Click to see the faces of parallelopiped.
(Here all the faces are square) (Here all the faces are rectangular)
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Area of base (square) = a x b
a
Height of cube = c
Volume of cube = Area of base x height
= (a x b) x c
b
c
b
Volume of Cuboid Click to animate
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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
Click to see
a
(unit)3
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Circumference of circle = 2 π r
Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)
r h
Outer Curved Surface area of cylinder
Activity -: Keep bangles of same radius one over another. It will form a 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
Click to animate
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Total Surface area of a solid 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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2πr
h
r
h
Surface area of cylinder = Area of rectangle= 2 πrh
Other method of Finding Surface area of cylinder with the help of paper
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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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Cone
Baser
h
l = Slant height
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3( V ) = π r2h
r
h h
r
Volume of a Cone Click to See the experiment
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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Mr. Mohan has only a little jar of juice he wants to distribute it to his three friends. This time he choose the cone shaped glass so that quantity of juice seem to appreciable.
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l
2πr
l
2πr
l
Area of a circle having sector (circumference) 2π l = π l 2
Area of circle having circumference 1 = π l 2/ 2 π l
So area of sector having sector 2 π r = (π l 2/ 2 π l )x 2 π r = π rl
Surface area of cone
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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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Surface area
6r2
=2 π r2
(about)
2π r2 2π r2 2 π r2
Volume r3 π r3 π /3 π r3 2/3 π r3
Area and volume of different geometrical figures
r/√2
r
l=2rr
r
r
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Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree
Click the next
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r
3r
V= 1/3π r2(3r)
V= π r3
Long but Light in weight
Small needle will require to stick it in the tree,so little harm in tree
V= π r2 (3r)
V= 3 π r3
Long but Heavy in
weight
Long needle will require to stick it in the tree,so much harm in tree
r
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Cone shape
Cylindrical shape
Bottle
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V1
r
V=1/3 πr2hIf h = r thenV=1/3 πr3
rr
If we make a cone having radius and height equal to the radius of sphere. Then a water filled cone can fill the sphere in 4 times.
V1 = 4V = 4(1/3 πr3) = 4/3 πr3
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4( 1/3πr2h ) = 4( 1/3πr3 ) = V
h=rr
Volume of a Sphere Click to See the experiment
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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Thanks
U.C. Pandey R.C.Rauthan, G.C.Kandpal