PowerPoint Presentation on Surface Area and Volume

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Slide 1

Slide show Mathematics Exercise 13 Surface Area and Volume Topic on On

Slide 2

Surface Area and Volume Vocabulary & Formulas

Slide 3

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.

Slide 4

Rectangular Prism Definition: A three-dimensional solid that has two congruent and parallel faces that are rectangles. The remaining faces are rectangles.

Slide 5

Cube Definition: A rectangular prism in which all faces are congruent squares.

Slide 6

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?

Slide 7

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?

Slide 8

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

Slide 9

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

Slide 10

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

Slide 11

Volume of a Cube Ex: How much sand would I need to fill the inside of a particular cube? Formula: V = s3

Slide 12

Surface area and volume of different Geometrical Figures Cube Parallelopiped Cylinder Cone

Slide 13

Total faces = 6 ( Here three faces are visible) Faces of cube

Slide 14

Faces of Parallelopiped Total faces = 6 ( Here only three faces are visible.)

Slide 15

Total cores = 12 ( Here only 9 cores are visible) Cores Note Same is in the case in parallelopiped.

Slide 16

Surface area = Area of all six faces = 6a2 a b Surface area Cube Parallelopiped 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)

Slide 17

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 Volume of Parallelopiped Click to animate

Slide 18

Volume of Cube Area of base (square) = a2 Height of cube = a Volume of cube = Area of base x height = a2 x a = a3 Click to see (unit)3

Slide 19

Circumference of circle = 2 π r Area covered by cylinder = Surface area of of cylinder = (2 π r) x( 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 Click to animate

Slide 20

Total Surface area of a solid cylinder =(2 π r) x( h) + 2 π r2 Area of curved surface + area of two circular surfaces = = 2 π r( h+ r)

Slide 21

Surface area of cylinder = Area of rectangle= 2 πrh Other method of Finding Surface area of cylinder with the help of paper

Slide 22

Volume of cylinder Volume of cylinder = Area of base x vertical height = π r2 xh

Slide 23

Cone

Slide 24

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

Slide 25

if both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone ,

Slide 26

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.

Slide 27

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

Slide 28

Comparison of Area and volume of different geometrical figures

Slide 29

Area and volume of different geometrical figures

Slide 30

Total surface Area and volume of different geometrical figures and nature 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. 22r

Slide 31

Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree Click the next

Slide 32

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 r

Slide 34

V=1/3 πr2h If h = r then V=1/3 πr3 r 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

Slide 35

4( 1/3πr2h ) = 4( 1/3πr3 ) = V h=r 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

Slide 36

Volume is the amount of space occupied by any 3-dimensional object. 1cm 1cm 1cm Volume = base area x height = 1cm2 x 1cm = 1cm2

Slide 37

Side 2 Bottom Back Top Side 1 Front Length (L) Breadth (B) Height (H) Cuboid

Slide 38

The net L L L L B H H H H L B B B B B H H

Slide 39

H B L H B H L L L H B L H B H 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 ) Total surface Area

Slide 40

Slide 41

Cube Volume = Base area x height = L x L x L = L3 L L L Total surface area = 2LxL + 2LxL + 2LxL = 6L2

Slide 42

2(LxB + BxH + LxH) LxBxH Cuboid 6L2 L3 Cube Sample net Total surface area Volume Figure Name

Slide 43

Show ends

Summary: this slide show is mase by abhinav kumarsinha class-9th-E school-k.v.no.2 ambala cantt

Tags: surface area and volume

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