Solid Convex Concave Regular Cylinder Prism Cone Pyramid Sphere Polyhedron a solid figure with many plane faces Solid a 3D shape that encloses space but is not made up of all polygon sides ID: 1044685
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1. 3-D ShapesConcept 52
2. PolyhedronSolidConvexConcaveRegularCylinderPrismConePyramidSphere
3. Polyhedron: a solid figure with many plane faces
4. Solid: a 3-D shape that encloses space but is not made up of all polygon sides.
5. Convex: all vertices of the solid push outward. Concave: one or more vertices of the solid are pushed inward.
6. Regular: a polyhedron with all the same regular polygons.
7. Prism: a polyhedron made up of two parallel bases connected by rectangles. Rectangular prismTriangular Prism Pentagonal Prism
8. Pyramid:
9. Cylinder:
10. Cone:
11. Sphere:
12. 1. 2. 3. 4.Determine whether each solid is a polyhedron or solid. Then draw a net for each if possible. ConePentagonal PrismSphereTriangular Prism
13. Given the net of a solid. Draw the solid and give its name.5.6.7.Triangular PrismHexagonal PyramidCube
14. Parts of Solids and Cross SectionConcept 53
15. Parts of a 3D Shape!Only cut this solid lineFold on all dotted lines.(fold both directions)
16. Triangular PyramidBase: a polygonBase:Edge: a segment where two faces come together.EdgeVertex: a point where three or more edges come together.Face: a set of polygons that make up the other surfaces of a polyhedron. (lateral faces)VertexVertexVertexVertexEdgeEdgeEdgeEdgeEdgeFaceFaceFace
17. Then identify the solid. If it is a polyhedron, name the faces, edges, and vertices.9.10.Faces:Edges:Vertices:Circle S (B)nonePoint RFaces:Edges:Vertices:Pentagons: PWXYX and QRSUV, Quadrilaterals: QVXW, UVXY, USZY, PRSZ, PRXW Points: P,W,X,Y, Z,Q,R,S,U,V
18. Then identify the solid. If it is a polyhedron, name the faces, edges, and vertices.11.Faces:Edges:Vertices:Triangles: ABC and DEF, Quadrilaterals: ABED, BCFE, ACFD Points: A, B, C, D, E, F
19. Cross Section: a surface or shape that is or would be exposed by making a straight cut through something, especially at right angles to an axis. Sketch the cross section from a vertical slice of each figure.1.2.3.
20. Describe each cross section.4.5.6.7.8.SquareRectangleTriangleOvalRectangle
21.
22. Euler’s TheoremConcept 54
23. There are 11 polyhedrons located around the room at each group of desks. Use each one to fill in a row of the table. If the shape has a name you know write it in the first column, otherwise just write what it is made up of. Ex. (2 triangles and 3 rectangles)
24. Name or what shapes make it.# of Faces# of Vertices# of Edges123456789101112
25. Euler’s TheoremF + V = E + 2
26. Examples: 8 faces and 18 edges21 edges and 14 vertices
27. 12 pentagon faces 8 triangle faces1 hexagon and 6 triangle faces
28. 20 triangle faces12 pentagon and 20 hexagon faces
29. 2 hexagons and 6 rectangles
30. Volume of PrismsConcept 55
31. Rectangular PrismTriangular Prism TrapezoidalPrismOtherPrismsVolume = Base Area height V = B h
32. Rectangular PrismsV = B h V = (9 5) 4 V = 180 V = B h V = (6 11) 2 V = 132
33. Triangular PrismV = B h V = (5) 14 V = 350 V = B h V = ( ) 9 V = 108
34. Trapezoidal PrismV = B h V = () 7 V = 77 V = () 7 V = B h V = () 15 V = 510 V = () 15
35. Other PrismsV = B h V = () 7 V = 655.2 V = () 7 V = B h V = () 4 V = 8360 V = () 4
36. Find the volume of the right prism.V = B h V = () V = 576 V = B h V = () V = V = B h V = () V = 18
37. Find the missing side length given the Volume, V of each solid. 4. V = 480 cm25. V = 120 in26. V = 180 cm2V = B h 480 = () 480 = 96x 5 cm = xV = B h 120 = () 12 in = x120 = 10xV = B h 180 = () 4 18 = x + 12180 =10(x +12)6 cm = x
38. Volume of PyramidsConcept 56
39. Volume of PyramidsSquarePyramid TriangularPyramidOtherPyramids
40. Volume of PyramidsVolume = Base Area height V = B h
41. Square Pyramids2.1.V = B h V = 8 V = V = B h V = 7 V =
42. Triangular Pyramids3.4.V = B h V = 7 V = V = B h V = V =
43. Other Pyramids5.6.V = B h V = V = V = B h V = V =
44. Find the volume of each pyramid. Round to the nearest tenth if necessary.V = B h V = V = V = B h V = V = V = B h V = V =
45. V = B h V = V =
46. Volume of Cylinders, cones, and spheresConcepts 57 - 59
47.
48.
49.
50.
51.
52. Find the volume of each.1. 2. 3.
53. 4. 5. 6.
54. 7. hemisphere: area of 8. 9.great circle ≈ 4π ft2