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# surface area and volume

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## surface area and volumePresentation Transcript

• Slide show
On
Mathematics
Exercise 13
Topic on
Surface Area and Volume
• Surface Area and Volume
Vocabulary & Formulas
• Prism
Definition:
A three-dimensional solid that has two congruent and parallel faces that are polygons. The remaining faces are rectangles. Prisms are named by their faces.
• Rectangular Prism
Definition:
A three-dimensional solid that has two congruent and parallel faces that are rectangles. The remaining faces are rectangles.
• Cube
Definition:
A rectangular prism in which all faces are congruent squares.
• Surface Area
Definition:
The sum of the areas of all of the faces of a three-dimensional figure.
Ex. How much construction paper will I need to fit on the outside of the shape?
• Volume
Definition:
The measure in cubic units of the interior of a solid figure; or the space enclosed by a solid figure.
Ex. How much sand will it hold?
• Surface Area of a Rectangular Prism
Ex:
How much construction paper would I need to fit on the outside of a particular rectangular prism?
Formula:
S.A. = 2LW + 2Lh + 2Wh
• Surface Area of a Cube
Ex:
How much construction paper would I need to fit on the outside of a particular cube?
Formula:
S.A. = 6s2
• Volume of a Rectangular Prism
Ex:
How much sand would I need to fill the inside of a particular rectangular prism?
Formula:
V = L*W*h
• Volume of a Cube
Ex:
How much sand would I need to fill the inside of a particular cube?
Formula:
V = s3
• Surface area and volume of different Geometrical Figures
Cube
Cylinder
Parallelopiped
Cone
• face
face
face
1
Dice (Pasa)
3
2
Faces of cube
Total faces = 6 ( Here three faces are visible)
• Face
Face
Face
Book
Brick
Faces of Parallelopiped
Total faces = 6 ( Here only three faces are visible.)
• Cores
Cores
Total cores = 12 ( Here only 9 cores are visible)
Note Same is in the case in parallelopiped.
• 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)
• Volume of Parallelopiped
Click to animate
c
b
b
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
• Volume of Cube
Click to see
a
a
a
Area of base (square) = a2
Height of cube = a
Volume of cube = Area of base x height
= a2 x a = a3
(unit)3
• Outer Curved Surface area of cylinder
r
r
h
Click to animate
Activity -: Keep bangles of same radius one over another. It will form a cylinder.
Circumference of circle = 2 π r
Formation of Cylinder by bangles
It is the area covered by the outer surface of a cylinder.
Circumference of circle = 2 π r
Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)
• Total Surface area of a solid cylinder
Curved surface
circular surfaces
Area of curved surface +
area of two circular surfaces
=
=(2 π r) x( h) + 2 π r2
= 2 π r( h+ r)
• r
Other method of Finding Surface area of cylinder with the help of paper
h
h
2πr
Surface area of cylinder = Area of rectangle= 2 πrh
• r
h
Volume of cylinder
Volume of cylinder = Area of base x vertical height
= π r2xh
• Cone
l = Slant height
h
Base
r
• 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) = π r2h
V = 1/3 π r2h
• 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
• 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.
• Surface area of cone
l
2πr
l
l
2πr
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
• Comparison of Area and volume of different geometrical figures
• Area and volume of different geometrical figures
r
r
r
r/√2
l=2r
r
• Total surface Area and volume of different geometrical figures and nature
r
r
r
l=3r
r
1.44r
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.
• Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree
Click the next
• 3r
r
r
V= 1/3π r2(3r)
V= π r3
Long but Light in weight
Small niddle 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 niddle will require to stick it in the tree,so much harm in tree
• Bottle
Cone shape
Cylindrical shape
• r
V1
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
V=1/3 πr2h
If h = r then
V=1/3 πr3
V1 = 4V = 4(1/3 πr3)
= 4/3 πr3
• Volume of a Sphere
Click to See the experiment
r
r
h=r
Here the vertical height and radius of cone are same as radius of sphere.
4( volume of cone) = volume of Sphere
4( 1/3πr2h) = 4( 1/3πr3 ) = V
V = 4/3 π r3
• Volume
is the amount of space occupied by any 3-dimensional object.
1cm
1cm
1cm
Volume = base area x height
= 1cm2 x 1cm
= 1cm2
• Back
Top
Side 2
Side 1
Front
Bottom
Cuboid
Back
Top
Side 2
Side 1
Front
Height (H)
Bottom
Length (L)
• The net
L
H
H
L
H
B
B
B
B
L
H
H
H
L
B
B
L
• Total surface Area
L
L
H
L
H
B
B
B
B
H
H
L
H
H
L
L
L
Total surface Area = L x H + B x H + L x H + B x H + L x B + L x B
= 2 LxB + 2BxH + 2LxH
= 2 ( LB + BH + LH )
• Cube
L
L
L
Volume = Base area x height
= L x L x L
= L3
• Total surface area = 2LxL + 2LxL + 2LxL
= 6L2
• Sample net
Total surface area
Volume
Figure
Name
6L2
L3
Cube
2(LxB + BxH + LxH)
LxBxH
Cuboid
• Show ends