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