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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.

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Solid Geometry

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  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

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