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Understanding Solid Geometric Figures: Volume and Area Formulas

This chapter covers solid geometric figures, focusing on calculating volumes and areas for common shapes such as cylinders, cones, pyramids, spheres, and prisms. You will learn the definitions and formulas necessary for determining volume (e.g., V = lwh for rectangular prisms) and area (e.g., A = 6s² for cubes). Additionally, we will discuss measurement systems, including customary and metric units, essential for real-world applications in geometry. By the end, you will be equipped to tackle problems involving geometric figures and conversions.

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Understanding Solid Geometric Figures: Volume and Area Formulas

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  1. MATH 3A GEOMTREY CHAPTER 11 POWER POINT PRESENTATION SOLID GEOMETRIC FIGURES AND THEIR MEASURES

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. GEOMETRIC SOLIDS

  8. Volume Formulas

  9. Another View

  10. 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)

  11. 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)

  12. 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

  13. 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

  14. Metric Conversions

  15. More Metric Conversions

  16. Metric Prefixes

  17. 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

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