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MATH 3A GEOMTREY CHAPTER 11 POWER POINT PRESENTATION SOLID GEOMETRIC FIGURES AND THEIR MEASURES.
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Transcript of MATH 3A GEOMTREY CHAPTER 11 POWER POINT PRESENTATION SOLID GEOMETRIC FIGURES AND THEIR MEASURES.
MATH 3A GEOMTREY CHAPTER 11 POWER POINT PRESENTATION
SOLID GEOMETRIC FIGURES AND THEIR MEASURES
LEARNING TARGETS
• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:
• CALCULATE BASIC VOLUMES FOR CYLINDERS, CONES, PYRAMIDS, SPHERES, PRISMS.
• CALCULATE AREAS FOR: CYLINDERS, CONES, PYRAMIDS, SPHERES, PRISMS.
• COMPLETE MEASUREMENTS FOR SOLID FIGURES.
What is Volume?
• Volume is a measure of the number of unit cubes in a solid figure. It is sometimes called capacity.
• Prism: A 3-D figure that has congruent polygons as bases, and whose sides are parallelograms.
• A Prism can be a: cube, a rectangular prism, or a triangular prism.
Cube
• Cube – a 3-D figure whose sides are all equal.• Volume formula: V = lwh or length times
width times height). You could also calculate side³. List answers in units cubed³
• Area formula: A = 6s². List answers in units squared.²
Triangular Prisms
• A triangular prism has 2 triangle bases, and three rectangle sides.
• Volume formula: V = Bh where B is the area of the base. Listed in units cubed³.
• Area formula: A = 2(area of triangle + h (a+b+c). List answers in units squared².
Rectangular Prism
• Has a longer base than height.• Volume formula: V = lwh (length times
wideth times height). Listed in units cubed³.• Area formula: 2(lw + hl + hw). Listed in units
squared².
GEOMETRIC SOLIDS
Volume Formulas
Another View
Surface Area Formulas
• Cube: 6s²• Rectangular Prism: 2(lw + hl + hw)• Right Prism: 2(area of triangle) + h(a + b + c)• Cylinder: 2πr² + (2πr)h• Pyramid: s² + 2sl (area of base + areas of 4
triangles)• Cone: πr(r + l) = πr² = 1/2bl (area of base plus
area of sides)
Measurement
• Customary: units that are common, ordinary used in the United States: inches/feet/yards/cups/ounces/gallons/pints/miles/pounds/ounces/tons,etc.
• Capacity: The amount a container will hold.• Metric: A system based on powers of ten:– Liquid: Liters (L), Capacity– Weight: Grams (g), Mass– Distance: Meters (m)
Common Conversions
• 1 foot = 12 inches• 1 yard = 36 inches• 3 feet = I yard• 1 mile = 5,280 feet• 1 cup = 8 fluid ounces• 2 cups = I pint• 2 pints = I quart• 4 quarts = I gallon
A few more…
• 1 pound = 16 ounces• 2,000 pounds = 1 ton• 12 months = I year• 60 minutes = I hour• 1 day = 24 hours• 1 year = 365 days• 1 mile = 1,760 yards• 1 acre = 43,560 sq. ft or 4,840 sq. yards
Metric Conversions
More Metric Conversions
Metric Prefixes
Metric Chart
• Kilo – Hecto – Deka Unit deci – centi – milli• km hm dam m,g,L dm cm mg
10g
• To convert: move the decimal forward or backward• Ex: 10 grams = 1.0 dekagrams