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Chapter 12 – Surface Area and Volume of Solids Section 12.1– Space Figures and Nets.

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Presentation on theme: "Chapter 12 – Surface Area and Volume of Solids Section 12.1– Space Figures and Nets."— Presentation transcript:

1 Chapter 12 – Surface Area and Volume of Solids Section 12.1– Space Figures and Nets

2 Section 12.1 Polyhedron – a 3-D figure whose surfaces are polygons. Face – individual polygon of the polyhedron. Edge – is a segment that is formed by the intersection of two faces. Vertex – is a point where three or more edges intersect.

3 Section 12.1 Net – a 2-D pattern that you can fold to form a 3-D figure. Euler’s Formula – the number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula: F + V = E + 2

4 CUBE: Net Drawing

5 CUBE: 3-Dimensional Faces Edge Vertex

6 CYLINDER: Net Drawing

7 CYLINDER: 3-Dimensional Faces Edge

8 TRIANGULAR PRISM: Net Drawing

9 TRIANGULAR PRISM: 3-Dimensional Faces Edge Vertex

10 RECTANGULAR PRISM: Net Drawing

11 RECTANGULAR PRISM: 3-Dimensional Faces Edge Vertex

12 HEXAGONAL PRISM: Net Drawing

13 HEXAGONAL PRISM: 3-Dimensional Faces Edge Vertex

14 TRIANGULAR PYRAMID: Net Drawing

15 TRIANGULAR PYRAMID: 3- Dimensional Slant Height Altitude

16 SQUARE PYRAMID: Net Drawing Slant Height

17 SQUARE PYRAMID: 3- Dimensional Slant Height

18 HEXAGONAL PYRAMID: Net Drawing

19 HEXAGONAL PYRAMID: 3- Dimensional Slant Height Altitude

20 Chapter 12 – Surface Area and Volume of Solids Section 12.2 – Surface Areas of Prisms and Cylinders

21 Section 12.2 Prism – is a polyhedron with exactly two congruent, parallel faces. Bases – two congruent, parallel faces of a prism. Lateral Faces – additional faces of a prism. Altitude – is a perpendicular segment that joins the planes of the bases.

22 Section 12.2 Height – the length of the altitude. Right Prism – the lateral faces are rectangles and a lateral edge is the altitude of the prism. Oblique Prism – at least one lateral face is not a rectangle. Lateral Area – is the sum of the area of the lateral faces.

23 CUBE: 3-Dimensional BASE LATERAL FACE

24 RECTANGULAR PRISM: 3-Dimensional BASE LATERAL FACE

25 TRIANGULAR PRISM: 3-Dimensional BASE LATERAL FACE

26 HEXAGONAL PRISM: 3-Dimensional BASE LATERAL FACE

27 OBLIQUE PRISM: 3-Dimensional BASE LATERAL FACE ALTITUDE

28 Section 12.2 Surface Area – the sum of the lateral area and the two bases. Theorem 10-1 – the lateral area of a right prism is the product of the perimeter of the base and the height. L.A. = ph The surface area of a right prism is the sum of the lateral area and the area of the 2 bases. S.A. = L.A. + 2B

29 Section 12.2 Cylinder – is a three-dimensional figure with exactly two congruent, parallel faces. Bases – two congruent, parallel faces of a cylinder are circles. Altitude – is a perpendicular segment that joins the planes of the bases.

30 CYLINDER: 3-Dimensional BASE

31 OBLIQUE CYLINDER: 3- Dimensional BASE ALTITUDE

32 Section 12.2 Surface Area – the sum of the lateral area and the two circular bases. Theorem – the lateral area of a right prism is the product of the circumference of the base and the height of the cylinder. L.A. = 2πrh or L.A. = πdh The surface area of a right prism is the sum of the lateral area and the area of the 2 bases. S.A. = L.A. + 2B or S.A. = 2πrh + 2πr 2

33 Chapter 12 – Surface Area and Volume of Solids Section 12.3 – Surface Areas and Pyramids and Cones

34 Moving from Prisms/Cylinders to Pyramids/Cones

35 Section 12.3 Pyramid – is a polyhedron in which one face can be any polygon and the other faces are triangles that meet at a common vertex. Bases – the only face of a pyramid that is not a triangle. Lateral Faces – triangles of pyramid. Vertex of a pyramid – the point where all lateral faces of a pyramid meet.

36 Section 12.3 Altitude – is a perpendicular segment from the vertex to the plane of the base. Height – the length of the altitude (h). Regular Pyramid – a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. Slant Height – is the length of the altitude of a lateral face of a pyramid. Lateral Area – is the sum of the area of the congruent lateral faces.

37 TRIANGULAR PYRAMID: 3- Dimensional Slant Height Altitude

38 SQUARE PYRAMID: 3- Dimensional Slant Height

39 HEXAGONAL PYRAMID: 3- Dimensional Slant Height Altitude

40 Section 12.3 Surface Area – the sum of the lateral area and the area of the base. Theorem – the lateral area of a regular pyramid is the half the product of the perimeter of the base and the slant height. L.A. = ½ pl The surface area of a regular pyramid is the sum of the lateral area and the area of the base. S.A. = L.A. + B

41 Section 12.3 Cone – is a “pointed” like a pyramid, but its base is a circle. Right Cone – the altitude is a perpendicular segment from the vertex to the center of the base. Bases – the only circle on a cone. Vertex of a cone – the only distinctive point on the object.

42 Section 12.3 Altitude – is a perpendicular segment from the vertex to the plane of the base. Height – the length of the altitude (h). Slant Height – is the distance from the vertex to a point on the edge of the base. Lateral Area – is ½ the perimeter (circumference) of the base times the slant height.

43 CONE: Net Drawing

44 CONE: 3-Dimensional

45 Section 12.3 Surface Area – the sum of the lateral area and the area of the base. Theorem – the lateral area of a right cone is the half the product of the circumference of the base and the slant height. L.A. = ½ 2  rl or  rl The surface area of a right cone is the sum of the lateral area and the area of the base. S.A. = L.A. + B

46 Chapter 12 – Surface Area and Volume Section 12.6 – Surface Area and Volumes of Spheres

47 Section 12.6 Sphere Set of all points equidistant from a given point. C

48 Section 12.6 Surface Area of a Sphere S = 4πr 2 C


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