3 -D Geometry
3-D Geometry(Volume & Surface Area)
Formula(s):Example 15:Find the approximate volume in square inches.Example 1:Find the volume.Example 16:Find the approximate volume in cubic feet.Measurement in 3-D Figures
Example 13:Find the approximate surface area in squareinches.Example 2:Find the volume.Example 14:Find the approximate volume in cubiccentimeters.Example 3:Find the volume. Use 3.14 for pi.Volume of Prisms & Cylinders
Formula(s)Example 4:Find the volume.Example 1 :Example 12:Find the surface area.Find the surface area. Use 3.14 for pi.Surface Area of Pyramids & Cones
Formula(S)Example 10:Find the surface area.Example 5:Example 6:Find the volume.Find the volume. Use 3.14 for pi.Volume of Pyramids & Cones
Formula(s)Example 7:Find the surface area.Example 8:Example 9:Find the surface area.Find the surface area. Use 3.14 for pi.Surface Area of Prisms & Cylinders
Answer Key!Note: I have written this answer key based on the formulasfound on the Florida FCAT 2.0 Reference Sheet.3-D Geometry(Volume & Surface Area)
Example 1:Formula(s)V BhFind the volume.V Bh*Remember B Area of BaseRectangularTriangularB bhB bh12V (bh)hV (3in 2in) 4inV 24in3CylinderB 𝜋r2Example 15:Example 16:Find the approximate volume in square inches.Find the approximate volume in cubic feet. 1.22 in 13.1 ft 4.72 in 5.6 ft 9.8 ftV BhV (𝜋r2)hV (3.14 1.222) 4.72inV 22.1in31V Bh13V (bh)h31V (9.8ft 5.6ft) 13.1 ft3V 239.6 ft3Measurement in 3-D Figures
Example 14:Example 13:Find the approximate volume in cubiccentimeters.Find the approximate surface area in squareinches. 0.59 in 5.08 cm 2.54 cm 15.24 cm 0.24 inSA 2𝜋r2 2𝜋rhSA 2(3.14)(0.592) 2(3.14)(0.59)(0.24)SA 2.19 0.89SA 3.08 in2V Bh1V ( bh)h2V (0.5)(2.54cm)(5.08cm)(15.24cm)V 98.3 cm3Example 2:Example 3:Find the volume.Find the volume. Use 3.14 for pi.V Bh1V ( bh)h2V (0.5)(8cm)(7cm)(13cm)V 364 cm2V BhV (𝜋r2)hV (3.14)(4.2mm)2(7.5mm)V 415.4mm3Volume of Prisms & Cylinders
Example 4:Formula(s)Find the volume.1V Bh3RectangularTriangularB bh1B 2bhConeB 𝜋r21V Bh3V (bh)h131V (5m)(6m)(7m)3V 70m3Example 1 :Example 12:Find the surface area.Find the surface area. Use 3.14 for pi.1SA 2Pl BSA 0.5(12 12 12)(6) 0.5(10.38)(12)SA 108 62.28SA 170.28 m21SA 2(2𝜋r)l BSA 𝜋rl 𝜋r2SA (3.14)(3)(10) 3.14(3)2SA 94.2 28.26SA 122.46 cm2Surface Area of Pyramids & Cones
Example 10:Formula(s)Find the surface area.Rectangular & TriangularPyramids1SA 2Pl B1ConeSA 2Pl BSA 0.5(4 4 4 4)(5) 4(4)SA 56in21SA 2(2𝜋r)l BP Perimeter of Basel slant heightB Area of BaseExample 5:Example 6:Find the volume.Find the volume. Use 3.14 for pi.1V Bh3V ( bh)h1 11V BhV ( )(9in)(5in)(8in)3V (𝜋r2)hV 60in3V (3.14)(4.2in)2(8in)3 21 13 21313V 147.7yd3Volume of Pyramids & Cones
Example 7:Formula(s)Find the surface area.Rectangular PrismSA 2bh 2bw 2hwTriangular PrismSA Ph 2BCylinderSA 2𝜋r2 2 𝜋rhSA 2bh 2bw 2hwSA 2(3)(4) 2(3)(2) 2(4)(2)SA 24 12 16SA 52 in2Example 9:Example 8:Find the surface area. Use 3.14 for pi.Find the surface area.SA Ph 2B1SA (10 12 14.9)(20) 2( )(14.9)(8)SA 738 119.2SA 857.2 mm22SA 2𝜋r2 2 𝜋rhSA 2(3.14)(3)2 2(3.14)(3)(4)SA 56.52 75.36SA 131.88 cm2Surface Area of Prisms &Cylinders
Lisa Davenport 2013Directions:Step 1: Print pages 1&2, 3&4, 5&6 front to back so that the printis facing in opposite directions.Step 2: Line up the pages as shown below.Step 3: Fold over the top half and secure with staples.The final product should look like this:
Find the volume. Surface Area of Pyramids & Cones Example 11: Find the surface area. Example 12: Find the surface area. Use 3.14 for pi. Example 4: Formula(s) Formula(S) . Answer Key! I have written this answer key based on the formulas found on the Florida FCAT 2.0 Reference Sheet. V Formula(s) Example 1: Find the volume.
course. Instead, we will develop hyperbolic geometry in a way that emphasises the similar-ities and (more interestingly!) the many differences with Euclidean geometry (that is, the 'real-world' geometry that we are all familiar with). §1.2 Euclidean geometry Euclidean geometry is the study of geometry in the Euclidean plane R2, or more .
www.ck12.orgChapter 1. Basics of Geometry, Answer Key CHAPTER 1 Basics of Geometry, Answer Key Chapter Outline 1.1 GEOMETRY - SECOND EDITION, POINTS, LINES, AND PLANES, REVIEW AN- SWERS 1.2 GEOMETRY - SECOND EDITION, SEGMENTS AND DISTANCE, REVIEW ANSWERS 1.3 GEOMETRY - SECOND EDITION, ANGLES AND MEASUREMENT, REVIEW AN- SWERS 1.4 GEOMETRY - SECOND EDITION, MIDPOINTS AND BISECTORS, REVIEW AN-
Analytic Geometry Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into: Plane Geometry is about flat shapes like lines, circles and triangles . shapes that can be drawn on a piece of paper S
geometry is for its applications to the geometry of Euclidean space, and a ne geometry is the fundamental link between projective and Euclidean geometry. Furthermore, a discus-sion of a ne geometry allows us to introduce the methods of linear algebra into geometry before projective space is
Mandelbrot, Fractal Geometry of Nature, 1982). Typically, when we think of GEOMETRY, we think of straight lines and angles, this is what is known as EUCLIDEAN geometry, named after the ALEXANDRIAN Greek mathematician, EUCLID. This type of geometry is perfect for a world created by humans, but what about the geometry of the natural world?
Geometry IGeometry { geo means "earth", metron means "measurement" IGeometry is the study of shapes and measurement in a space. IRoughly a geometry consists of a speci cation of a set and and lines satisfying the Euclid's rst four postulates. IThe most common types of geometry are plane geometry, solid geometry, nite geometries, projective geometries etc.
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