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Surface Area and Volume of Three-Dimensional Figures

Learn about three-dimensional figures and nets, polyhedrons, prisms, cylinders, pyramids, cones, and spheres. Explore how to find surface area and volume using formulas and understand the properties of each shape.

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Surface Area and Volume of Three-Dimensional Figures

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  1. Chapter 12 PPT Surface Area and Volume Prepared by Mrs. Pullo for her Geometry Students

  2. Three-Dimensional Figures and Nets A net is a two-dimensional pattern that you can fold to form a three-dimensional figure. A polyhedron is a three-dimensional figure whose surfaces are polygons. The polygons are the faces of the polyhedron. An edge is a segment that is the intersection of two faces. A vertex is a point where edges intersect. faces edge vertex

  3. Surface Areas of Prisms and Cylinders A prism is a polyhedron with two congruent, parallel bases. The other faces are lateral faces. A prism is named for the shape of its bases. An altitude of a prism is a perpendicular segment that joins the planes of the bases. The heighth of the prism is the length of an altitude. Like a prism, a cylinder has two congruent parallel bases. The bases of a cylinder are circles. An altitude of a cylinder is a perpendicular segment that joins the planes of the bases. The heighth of a cylinder is the length of an altitude. Base Base Base Base

  4. Lateral and Surface Areas of a Right Prism Total Surface are = Lateral area + 2 times the area of the bases (T = L + 2B) The Lateral area = Perimeter of base x height of the polyhedron 2B = area of the base times 2 because there are two bases in a prism

  5. Lateral and Surface Areas of a Right Cylinder Total Surface Area = L + 2B L = P h Perimeter is circumference in a circle L = 2Πrh T = 2 Πrh + 2 Πr2

  6. Surface Areas of Pyramids and Cones Lateral Area Surface Area L = ΠrlT = Πrl+ Πr2 Lateral Area Surface Area L = ½Pl T =½Pl + B

  7. Volumes of Prisms and Cylinders This is a trapezoidal prism because it base is a trapezoid V V= 1/2h(b + b) times height of object

  8. Volume of a Rectangular Prism V = Bh B = length times width So, V = lwh example

  9. Volume of a Cylinder V= Bh B = Πr2 V = Πr2 h example

  10. Volumes of Prisms and Cylinders - Example

  11. Volumes of Pyramids and Cones Slant height Slant height example

  12. Volumes of Pyramids and Cones - Example

  13. Surface Areas and Volumes of Spheres Fin Sub T 523 The

  14. In a Nut Shell Volume is the area of the base times the  ⊥ height in a prism and 1/3 of the area of the base times the ⊥ height in a pyramid or cone Finding the area of the base depends on the shape Surface area is the lateral area plus the area of the base(s) Lateral area is the perimeter of the base times the ⊥ height And the area of the bases depends on the shape of the base

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