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Surface Area And Volume

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Its a ppt on Mensuration - 3D Figures.
Surface area and volumes

Surface Area And Volume

  1. 1. The surface area of a solid object is the total area of the object's faces and curved surfaces. SURFACE AREA
  2. 2. Volume is the space that a substance or shape occupies or contains. VOLUME
  3. 3. SOME SOLID FIGURES
  4. 4. CUBE :- A cube is a three dimensional figure, with six faces, all faces in the shape of Square.
  5. 5. Lateral Surface Area of cube :- Lateral surface area refers to the area of only the walls ( it does not include the area of the floor and roof). Formula :- 4 a² Derivation :- Since all the sides of cube are in the shape of square. area of the square= a² no. of squares=4 area = 4a² (a=side)
  6. 6. Total Surface Area Of Cube :- Formula :- 6a² Derivation :- Since all the faces of a cube are squares , Area of square = a² No. of squares = 6 Area of 6 square = Total surface area of cube = 6a² Therefore , total surface area of the cube is 6a² .
  7. 7. Volume Of Cube : - Volume of the cube refers to the space inside the six walls. Formula :- a * a* a = a³ Unit :- unit³ (a=side)
  8. 8. CUBOID :- Cuboid is a three dimensional figure, with six sides and all sides of equal length. In Cuboid opposite rectangles are equal. Its three dimensions are - 1.Length(l) 2. Breadth (b) l b h
  9. 9. LATERAL SURFACE AREA:- Lateral surface area of the cuboid refer to the area of the four walls of it. Formula :- 2(l+b) h Derivation :- Area of rectangle1 = l*h Area of rectangle2 = b*h Area of rectangle3 = l*h Area of rectangle 4 = b*h Total area =2lh+2bh l b h
  10. 10. TOTAL SURFACE AREA:- Formula :- 2(lb + bh + hl ) Derivation Area of rectangle 1 (= lh)+ Area of rectangle 2 (=lb )+ Area of rectangle 3 (=lh )+ Area of rectangle 4 (=lb )+ Area of rectangle 5 (=bh )+ Area of rectangle 6 (= bh ) = 2(l*b ) + 2 ( b*h ) + 2 (l*h ) = 2 ( lb + bh + hl )
  11. 11. CYLINDER :- A right circular cylinder is a solid generated by the revolution of a rectangle about one of its side. It is a folded rectangle with h r
  12. 12. CURVEDSURFACEAREAOFCYLINDER:- Curved surface area of the cylinder :- = Area of the rectangular sheet = length * breadth = perimeter of the base of the cylinder* h = 2πr * h = 2πrh
  13. 13. TOTALSURFACEAREAOF CYLINDER:- Total surface area of a cylinder : = area of the rectangular sheet + 2 (area of the circular regions) = perimeter of the base of cylinder* h + 2 (area of circular base) = 2πrh + 2πr² = 2 πr ( r + h) h r
  14. 14. VOLUMEOFCYLINDER:- Volume of a cylinder can be built up using circles Of same size. So, the volume of cylinder can be obtained as :- base area * height = area of circular base * height = πr²h r
  15. 15. RIGHTCIRCULARCONE:- If a right angled triangle is revolved about one of its sides containing a right angle, the solid , thus formed is called a right circular cone. l is the slant height of the cone. l h r
  16. 16. CURVEDSURFACEAREAOFCONE:- It is the area of the curved part of the cone. (Excluding the circular base ) Formula :- 1/2* perimeter of the base* slant height = ½ * 2πr * l = πrl l r
  17. 17. TOTALSURFACEAREAOF CONE:- Total surface area of the cone :- Curved surface area of cone + circular base ( Red colored area + green colored area ) =πrl + πr² =πr ( l + r ) hh h l r
  18. 18. VOLUMEOFTHECONE:- Formula :- 1/3 πr²h Derivation :- If a cylinder and cone of same base radius and height are taken , and if cone is put under the cylinder then it will occupy only one –third part of it . Therefore, volume of cone is 1/3 of the hh 1 2 3 h l r
  19. 19. SPHERE: - The solid generated by revolving a circular lamina about any of its diameters, is called a sphere . The centre and radius of this circle are called respectively the centre and the radius of the sphere. A line segment passing r
  20. 20. SURFACEAREAOF SPHERE: - 4πr² Volume of sphere : - 4/3πr³ r
  21. 21. HEMISPHERE:- A plane passing through the centre of a sphere divides the sphere into two equal parts . Each part is known as hemisphere. r
  22. 22. CURVEDSURFACEAREAOF HEMISPHERE Formula : - 2πr² Derivation :- Since, hemisphere is half of sphere- Therefore, Surface area of sphere = 4πr² Half of it = 2πr² r
  23. 23. TOTALSURFACEAREAOF HEMISPHERE: Total surface area of hemisphere: = Curved surface area + circular base = 2πr² + πr² r
  24. 24. VOLUME OF HEMISPHERE: Volume of hemisphere = 1/2 * volume of sphere = 1/2 * 4/3*Пr³ r
  • TarunSharma753

    Mar. 28, 2020
  • HamiduAbbass

    Feb. 4, 2020
  • MananAmbaliya

    Feb. 28, 2017
  • silverben146

    Nov. 7, 2015

Its a ppt on Mensuration - 3D Figures. Surface area and volumes

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