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In Glorious 3-D!

In Glorious 3-D!. Most of the figures you have worked with so far have been confined to a plane—two-dimensional. Solid figures in the “real world” have 3 dimensions: length, width, and height. Polyhedron.

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In Glorious 3-D!

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  1. In Glorious 3-D! Most of the figures you have worked with so far have been confined to a plane—two-dimensional. Solid figures in the “real world” have 3 dimensions: length, width, and height.

  2. Polyhedron A solid formed by polygons that enclose a single region of space is called a polyhedron.

  3. Parts of Polyhedrons • Polygonal region = face • Intersection of 2 faces = edge • Intersection of 3+ edges = vertex edge face vertex

  4. Surface Area of Prisms, Cylinders Objectives: • To find and use formulas for the lateral and total surface area of prisms, cylinders, pyramids, and cones

  5. Prism A polyhedron is a prismiff it has two congruent parallel bases and its lateral faces are parallelograms.

  6. Classification of Prisms Prisms are classified by their bases.

  7. Right & Oblique Prisms Prisms can be right or oblique. What differentiates the two?

  8. Right & Oblique Prisms In a right prism, the lateral edges are perpendicular to the base.

  9. Pyramid A polyhedron is a pyramid iff it has one base and its lateral faces are triangles with a common vertex.

  10. Classification of Pyramids Pyramids are also classified by their bases.

  11. Pyramid A regular pyramid is one whose base is a regular polygon.

  12. Pyramid A regular pyramid is one whose base is a regular polygon. • The slant height is the height of one of the congruent lateral faces.

  13. Cylinder A cylinder is a 3-D figure with two congruent and parallel circular bases. • Radius = radius of base

  14. Nets Imagine cutting a 3-D solid along its edges and laying flat all of its surfaces. This 2-D figure is a net for that 3-D solid. An unfolded pizza box is a net!

  15. Nets Imagine cutting a 3-D solid along its edges and laying flat all of its surfaces. This 2-D figure is a net for that 3-D solid.

  16. Exercise 1 There are generally two types of measurements associated with 3-D solids: surface area and volume. Which of these can be easily found using a shape’s net?

  17. Surface Area The surface area of a 3-D figure is the sum of the areas of all the faces or surfaces that enclose the solid. • Asking how much surface area a figure has is like asking how much wrapping paper it takes to cover it.

  18. Lateral Surface Area The lateral surface area of a 3-D figure is the sum of the areas of all the lateral faces of the solid. • Think of the lateral surface area as the size of a label that you could put on the figure.

  19. Exercise 2 What solid corresponds to the net below? How could you find the lateral and total surface area?

  20. Exercise 3 Draw a net for the rectangular prism below. A B D C To find the lateral surface area, you could: • Add up the areas of the lateral rectangles

  21. Exercise 3 Draw a net for the rectangular prism below. Height of Prism Perimeter of the Base To find the lateral surface area, you could: • Find the area of the lateral surface as one, big rectangle

  22. Exercise 3 Draw a net for the rectangular prism below. Height of Prism Perimeter of the Base To find the total surface area, you could: • Find the lateral surface area then add the two bases

  23. Exercise 4 Find the lateral and total surface area.

  24. Exercise 5 Draw a net for the cylinder. Notice that the lateral surface of a cylinder is also a rectangle. Its height is the height of the cylinder, and the base is the circumference of the base.

  25. Exercise 6 Write formulas for the lateral and total surface area of a cylinder.

  26. Exercise 7 The net can be folded to form a cylinder. What is the approximate lateral and total surface area of the cylinder?

  27. Height vs. Slant Height By convention, h represents height and l represents slant height.

  28. Exercise 8 Draw a net for the square pyramid below. To find the lateral surface area: • Find the area of one triangle, then multiply by 4

  29. Exercise 8 Draw a net for the square pyramid below. To find the lateral surface area: • Find the area of one triangle, then multiply by 4

  30. Exercise 8 Draw a net for the square pyramid below. To find the total surface area: • Just add the area of the base to the lateral area

  31. Surface Area of a Pyramid Lateral Surface Area of a Pyramid: • P = perimeter of the base • l = slant height of the pyramid Total Surface Area of a Prism: • B = area of the base

  32. Exercise 9 Find the lateral and total surface area.

  33. Tons of Formulas? Really there’s just two formulas, one for prisms/cylinders and one for pyramids/cones.

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