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### Surface areas and volumes

• 1. Assignment (FA-3) Submitted to :- Sh. BharatBhushan Sir Submitted by :- Nitin Chhaperwal Class IX Roll No. 915 Kendriya Vidyalaya SSTPS Topic – Surface Areas and Volumes
• 4. face face face Total faces = 6 ( Here three faces are visible) 1 2 3 Dice (Pasa) Faces of cube
• 5. Faces of Parallelopiped Brick Book Face Face Face Total faces = 6 ( Here only three faces are visible.)
• 6. Cores Total cores = 12 ( Here only 9 cores are visible) Cores Note Same is in the case in parallelopiped.
• 7. Surface area = Area of all six faces = 6a2 a b 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)
• 8. 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
• 9. 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
• 11. Circumference of circle = 2 π r Area covered by cylinder = Surface area 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
• 12. 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)
• 13. 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
• 14. Volume of cylinder Volume of cylinder = Area of base x vertical height = π r2 x h r h
• 16. 3( V ) = π r2 h 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 r2 h
• 17. 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
• 18. 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.
• 19. 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
• 20. Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree? Click the next
• 21. 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 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 r
• 23. 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
• 24. 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.
• 25.
• 26. V1 r V=1/3 πr2 h 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
• 27. 4( 1/3πr2 h ) = 4( 1/3πr3 ) = V h=r r 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
• 28. The surface area of a sphere is four times the area of a great circle. ≈ 50.3 units2
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