1 / 51

Solid Geometry

Solid Geometry. Solid Geometry is the geometry of three-dimensional space It is called three-dimensional , or 3D because there are three dimensions: width, depth and height. Three Dimensions. A geometric object with flat faces and straight edges. each face is a polygon.

olaf
Télécharger la présentation

Solid Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Solid Geometry

  2. Solid Geometry is the geometry of three-dimensional space It is called three-dimensional, or 3D because there are three dimensions: width, depth and height. Three Dimensions

  3. A geometric object with flat faces and straight edges. each face is a polygon. Polyhedron

  4. FACE:Polygon shaped sides of a polyhedron EDGE: Line segment formed by intersection of two faces VERTEX: Point where three or more edges meet Polyhedron

  5. The surface that a solid object stands on or the bottom line of a shape such as a triangle or rectangle. Base

  6. Just like a 2D polygon a Polyhedron can be regular Polyhedron

  7. …or Irregular Polyhedron

  8. A Polyhedron can also be semi-Regular Polyhedron

  9. Just like a 2D polygon, a polyhedron can be convex Polyhedron

  10. …or concave Polyhedron

  11. A solid object that has two identical bases and all flat sides. The shape of the bases give the prism it’s name "triangular prism“ It is a polyhedron. Prism

  12. A solid object where:* The base is a polygon (a straight-sided shape)* The sides are triangles which meet at the top (the apex).It is a polyhedron. Pyramid

  13. A cylinder is a solid object with: * two identical flat circular (or elliptical) ends * and one curved side. Cylinder

  14. A solid (3-dimensional) object that has a circular base and one vertex Cone

  15. A solid (3-dimensional) object that has one curved side Sphere

  16. Prisms & Pyramids

  17. Three Dimensional Figures with Curved Surfaces

  18. VOLUME

  19. V=Bh B: Area of the base h: height/length of the prism Prism

  20. V=Bh V= (Area of Triangle) * h V= (½bh) * h V= (½*19*24) *47 V=(228) * 47 V= 10,716 cm3 Prism

  21. V=Bh V= (Area of Rect.) * h V= (bh) * h V= (2 * 3) * 6 V=(6) * 6 V= 36 ft3 Prism

  22. V=Bh B: Area of the base h: height/length of the prism Cylinder

  23. V=Bh V= (Area of Circle) * h V= (πr2) * h V= (π * 32) *10 V=(π * 9) * 10 V= (28.26) * 10 V= 282.6 cm3 Cylinder

  24. V=Bh V= (Area of Circle) * h V= (πr2) * h V= (π * 52) *21 V=(π * 25) * 21 V= (78.5) * 21 V= 1,648.5 ft3 Cylinder

  25. V=1/3Bh B: Area of the base h: height/length of the prism Pyramid

  26. V=1/3Bh V= 1/3(Area of Tri.) * h V= 1/3 * (½bh) * h V= 1/3 * (½* 6 * 4) *5 V= 1/3 * (12) * 5 V= 1/3 * 60 V= 20 cm3 Pyramid

  27. V=1/3Bh V= 1/3(Area of Sq.) * h V= 1/3 * (b * h) * h V= 1/3 * (5 * 5) *10 V= 1/3 * (25) * 10 V= 1/3 * 250 V= 250/3 units3 Pyramid

  28. V=1/3Bh B: Area of the base h: height/length of the prism Cone

  29. V=1/3Bh V= 1/3(Area of Circle)* h V= 1/3(πr2) * h V= 1/3(π * 1.52) *5 V=1/3(π * 2.25) * 5 V= 1/3(7.065) * 5 V= 11.78 in3 Cone

  30. V=1/3Bh V= 1/3(Area of Circle)* h V= 1/3(πr2) * h V= 1/3(π * 82) * 22 V= 1/3(π * 64) * 22 V= 1/3(200.96) * 22 V= 1,473.71 cm3 Cone

  31. V=4/3 πr3 Sphere

  32. V=4/3 πr3 V= 4/3 πr3 V= 4/3* π * 143 V= 4/3* π * 2744 V= 4/3* 8,616.16 V= 11,488.21 cm3 Sphere

  33. V=4/3 πr3 V= 4/3 πr3 V= 4/3* π * 33 V= 4/3* π * 27 V= 4/3* 84.78 V= 113.04 cm3 Sphere

  34. SURFACE AREA

  35. The sum of the area of the bases and lateral surfaces Surface Area

  36. SA=2B+Ph B: Area of the base P: Perimeter of a base h: height/length of the prism Right Prism

  37. SA=2B+Ph SA=2(Area of Rect.)+Ph SA= 2(bh) + Ph SA=2(3*2)+ (3+2+3+2)5 SA=2(6) + (10)5 SA= 12 + 50 SA= 62 cm2 Right Prism

  38. SA=2B+Ph SA=2(Area of Tri.)+Ph SA= 2(1/2bh) + Ph SA=2(1/2*3*8) + (3+8+√73)7 SA=2(12) + (11+√73)5 SA= 24 + 55 + 5√73 SA= 79 + 5√73 m2 SA = 121.72 m2 Right Prism

  39. SA=2B+Ch B: Area of the base C: Circumference of a base h: height/length of the cylinder Right Cylinder

  40. SA=2B+Ch SA=2(Area of Circ.)+Ch SA= 2(πr2) + (2πr)h SA=2(π*152)+(2*π*15)48 SA= 2(225π) + (30π)48 SA= 1413 + 4521.6 SA= 5934.6 cm2 Right Cylinder

  41. SA=2B+Ch SA=2(Area of Circ.)+Ch SA= 2(πr2) + (2πr)h SA=2(π*32)+(2*π*3)*9 SA= 2(9π) + (6π)*9 SA= 56.52 + 169.56 SA= 226.08 cm2 Right Cylinder

  42. SA=B + ½Ps B: Area of the base P: Perimeter of a base s: slant height of the lateral side Right Pyramid

  43. What is “slant height”? Right Pyramid (& Cone)

  44. SA=B + ½Ps SA=(Area of Rect.)+½Ps SA= (bh) + ½Ps SA=(12*12) + ½(12+12+12+12)*√136 SA= (144) + ½ (48)*√136 SA= 144 + 24√136 SA= 423.89 units2 Right Pyramid

  45. SA=B + ½Ps SA=(Area of Rect.)+½Ps SA= (bh) + ½Ps SA=(16*10) + ½(16+10+16+10)* 17 SA= (160) + ½ (52)*17 SA= 160 + 442 SA= 602 in2 Right Pyramid 10 in

  46. SA=B + ½Cs B: Area of the base P: Circumference of a base s: slant height of the lateral side Right Cone

  47. SA=B + ½Cs SA=(Area of Circ.)+½Cs SA= (πr2) + ½(2πr)s SA= (πr2) + (πr)s SA=(π62) + (π6)10 SA= 36π + 60π SA= 96π SA= 301.59 in2 Right Cone

  48. SA=B + ½Cs SA=(Area of Circ.)+½Cs SA= (πr2) + ½(2πr)s SA= (πr2) + (πr)s SA=(π0.62) + (π0.6)2 SA= .36π + 1.2π SA= 1.56π SA= 4.9 ft2 Right Cone

  49. SA=4πr2 r: radius Sphere

  50. SA=4πr2 SA= 4πr2 SA= 4*π*42 SA= 4*π*16 SA= 64π SA= 200.96 units2 Sphere

More Related