Surface area and volume of different Geometrical Figures

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Surface area and volume of different Geometrical
Figures
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Faces of cube
Total faces 6 ( Here three faces are visible)
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Faces of Parallelopiped
Total faces 6 ( Here only three faces are
visible.)
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Cores
Total cores 12 ( Here only 9 cores are visible)
Note ?Same is in the case in parallelopiped.
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Surface area
Cube
Parallelopiped
c
a
b
a
a
Click to see the faces of parallelopiped.
a
(Here all the faces are rectangular)
(Here all the faces are square)
Surface area Area of all six faces
6a2
Surface area Area of all six faces
2(axb bxc cxa)
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Volume of
Parallelopiped
Click to animate
a
Area of base (square) a x b
Height of cube c
Volume of cube Area of base x height
(a x b) x c
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Volume of Cube
Click to see
Area of base (square) a2
Height of cube a
Volume of cube Area of base x height
a2 x a a3
(unit)3
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Outer Curved Surface area of
cylinder
Click to animate
Activity - Keep bangles of same radius one over
another. It will form a cylinder.
Circumference of circle 2 p r
Formation of Cylinder by bangles
It is the area covered by the outer surface of a
cylinder.
Circumference of circle 2 p r Area covered by
cylinder Surface area of of cylinder (2 p
r) x( h)
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Total Surface area of a solid cylinder
Area of curved surface
area of two circular surfaces

(2 p r) x( h) 2 p r2
2 p r( h r)
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Other method of Finding Surface area of
cylinder with the help of paper
Surface area of cylinder Area of rectangle 2
prh
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Volume of
cylinder
Volume of cylinder Area of base x vertical
height p r2 xh
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Cone
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Volume of a Cone
Click to See the experiment
h
h
Here the vertical height and radius of cylinder
cone are same.
r
r
3( volume of cone) volume of cylinder
3( V ) p r2h
V 1/3 p 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 ,
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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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Surface area of cone
Area of a circle having sector (circumference)
2p l p l 2 Area of circle having circumference
1 p l 2/ 2 p l So area of sector having sector
2 p r (p l 2/ 2 p l )x 2 p r p rl
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Comparison of Area and volume of
different geometrical figures
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Area and volume of
different geometrical figures
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Total surface Area and volume of
different geometrical figures and nature
2?2r
So for a given total surface area the volume
of sphere is maximum. Generally most of the
fruits in the nature are spherical in nature
because it enables them to occupy less space but
contains big amount of eating material.
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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
r
V 1/3p r2(3r) V p r3 Long but Light in weight
Small niddle will require to stick it in the
tree,so little harm in tree
V p r2 (3r) V 3 p r3 Long but Heavy in
weight Long niddle will require to stick it in
the tree,so much harm in tree
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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.
r
r
V1/3 pr2h If h r then V1/3 pr3
V1 4V 4(1/3 pr3) 4/3 pr3
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Volume of a Sphere
Click to See the experiment
hr
Here the vertical height and radius of cone
are same as radius of sphere.
4( volume of cone) volume of Sphere
4( 1/3pr2h ) 4( 1/3pr3 ) V
V 4/3 p r3
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Thanks
U.C. Pandey R.C.Rauthan, G.C.Kandpal