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Published byWarren Morgan Modified over 8 years ago
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Opener
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UNIT EQ: HOW DO YOU CALCULATE THE SURFACE AREA AND VOLUME OF A 3-DIMENSIONAL FIGURE Surface Area & Volume
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ESSENTIAL QUESTION: WHAT ARE THE PARTS OF A POLYHEDRON? Space Figures
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Nets A net is a 2-dimensional pattern that you can fold to form a 3-dimensional figure. Which one?
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Draw & Label a net for this box:
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Polyhedron
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Euler’s Formula (Oiler) F = V = E =
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Cross Sections:
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Examples
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Cross Sections: Vertical Plane? Horizontal Plane? Diagonal Plane?
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Different Cross Sections? How many different polygonal cross-sections can you create?
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Openers:
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ESSENTIAL QUESTION: HOW DO YOU FIND THE SURFACE AREA AND VOLUME OF PRISMS AND CYLINDERS? Surface Area of Prisms & Cylinders
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Vocabulary PRISM – A polyhedron with exactly two parallel and congruent faces, called bases. The other faces are lateral faces. An altitude is a segment that is perpendicular to both bases. The height is the length of the altitude.
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Right vs. Oblique What shape are the Lateral Faces of each?
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Surface Area The lateral area is the sum of the areas of the lateral faces. The surface area is the sum of the areas of the lateral faces and the bases.
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Use the net to find Surface Area:
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Formulas for Surface Area:
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Find the Lateral and Surface Areas:
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Cylinders Cylinders have two congruent and parallel bases that are circles.
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Lateral & Surface Areas:
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Example:
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Opener
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ESSENTIAL QUESTION: HOW DO YOU FIND THE SURFACE AREA AND VOLUME OF PYRAMIDS AND CONES? Surface Area of Pyramids & Cones
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Vocabulary Base vs Lateral edges Height vs. SLANT Height
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Lateral Area & Surface Area
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Find the Surface Area of a Square Pyramid with base edges 5 cm and height of 3 cm.
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Cones Height vs. Slant Height Lateral Area: (½ pl) Surface Area: (LA + B)
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Opener Find Lateral & Surface Areas:
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ESSENTIAL QUESTION: HOW DO YOU FIND THE SURFACE AREA AND VOLUME OF PRISMS AND CYLINDERS? Volume of Prisms & Cylinders
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Volume
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Cavalieri’s Principle
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Volume of Prisms Rectangular Prisms: Area of Base x Height Cavalieri allows formula to extend to ANY Prism!
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Volume of a Prism
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Cylinders If V = Bh, then what is the area of the base of a generic Cylinder?
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Examples:
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Volume of Composite Figures: Volume Addition Postulate
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Opener
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ESSENTIAL QUESTION: HOW DO YOU FIND THE SURFACE AREA AND VOLUME OF PYRAMIDS AND CONES? Volume of Pyramids & Cones
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Volume of a Pyramid? Prism: A = phV = Bh Pyramid:A = ½ phV =
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Cones are just like Pyramids!
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Examples
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Opener
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ESSENTIAL QUESTION: HOW DO YOU FIND THE SURFACE AREA AND VOLUME OF SPHERES? Spheres
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Sphere A sphere is the set of all points in space equidistant from a point called the center. A sphere has a radius from the center to the sphere, and a diameter is any segment through the center with both endpoints on the sphere. A sphere can be cut into hemispheres, Whose cross-section is a great circle.
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Sphere Surface Area Area Formula?
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Examples:
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Sphere Volume:
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Volume of a Sphere
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Volume to Surface Area! If the Volume of a Sphere is 5,000in 3 then what is the Sphere’s Surface Area?
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L – A – V If two solids are SIMILAR and the ratio of similarity is ¾ then what would be the ratios for the following: L engths: Surface A reas: V olumes:
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ESSENTIAL QUESTION: HOW DO YOU FIND SURFACE AREA AND VOLUME OF SIMILAR 3-D FIGURES COMPARE? Similar Solids
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Similar Solids have the same shape and proportional dimensions. The ratio between corresponding edges is the similarity ratio.
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Are the following solids Similar? If so, give the similarity ratio:
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Similar? Similarity Ratio: Surface Areas: Surface Area Ratio: Volumes: Volume Ratio:
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Two Cubes Two cubes have volumes 729 cm 3 and 1331 cm 3. Find their ratio of Similarity and their Surface Area ratio.
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Example:
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