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