Surface areas and volumes
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Transcript of Surface areas and volumes
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Assignment (FA-3)
Submitted to :- Sh. BharatBhushan SirSubmitted by :- Nitin Chhaperwal Class IX Roll No. 915 Kendriya Vidyalaya SSTPS
Topic – Surface Areas and Volumes
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Contents :-
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CUBE AND CUBOID
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faceface
face
Total faces = 6 ( Here three faces are visible)
1
2 3
Dice (Pasa)
Faces of cube
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Faces of Parallelopiped
BrickBook
Fac
e
Face
Face
Total faces = 6 ( Here only three faces are visible.)
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Cores
Total cores = 12 ( Here only 9 cores are visible)
Cores
Note Same is in the case in parallelopiped.
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Surface area = Area of all six faces
= 6a2
ab
Surface area
Cube Parallelopiped (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 (rectangle) = a x b
a
Height of cuboid = c
Volume of cube = Area of base x height
= (a x b) x c
b
c
b
Volume of Parallelopiped 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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CYLINDER
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Circumference of circle = 2 π r
Area covered by cylinder = Surface area of cylinder = (2 π r) x( h)
rh
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 x h
r
h
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Baser
h
l = Slant height CONE
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3( V ) = π r2h
r
h h
r
Volume of a ConeClick 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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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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SPHERE
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A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.
Sphere
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The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.
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V1
r
V=1/3 πr2h
If h = r then
V=1/3 πr3
r
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
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
Click to See the experiment
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The surface area of a sphere is four times the area of a great circle.
50.3 units2
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THANK YOU