Geometric MeasurementsGeometric Measurements

Christine Knobbe

base

circumference

length

height

Microsoft Office Word 97 - 2003 Document

Shapes vs. FiguresShapes vs. Figures

What are the basic geometric shapes?◦Square◦Triangle◦Circle

What are the basic geometric figures?◦Cube◦Prism◦Pyramid◦Cone◦Sphere◦Cylinder

Types of measurementTypes of measurementWhat types of terms are associated

with geometric measurements?◦Area◦Perimeter◦Circumference

◦Volume◦Surface Area

Do you remember the formulas?◦Discuss with a partner

Why are these separated?

FormulasFormulasArea

◦A = L*W, A = r2

Perimeter◦P = 2L + 2W

Circumference◦C = 2r

Volume◦V=bh, where b is the area of the base

Surface Area◦S = sum of area of all sides

These vary depending on what shape the base is.

Formula ExceptionsFormula Exceptions

The volume of a couple of geometric figures is tricky! Which are they?◦Pyramids and Cones

Why do you think so?◦ They come to a point instead of staying the

same shape the entire length like a prism

◦V = 1/3 bh

Practice ProblemsPractice ProblemsGet into small groups (3-4)Find the following for each figure:

◦Surface Area◦Volume

7 cm 2 in

5 in

24 m

100 m

Practice SolutionsPractice SolutionsOnly one dimension is given

◦So it must be a cubeSurface area

◦S = sum of area of all sides◦S = 72 + 72 + 72 + 72 + 72 + 72

◦S = 6 * 72 = 294 cm2

Volume◦V = bh = L*W*h◦V = 7 * 7 * 7 = 343 cm3

7 cm

Volunteers?

Practice SolutionsPractice Solutions

24 m

100 m

Volunteers?

Surface area◦S = sum of area of all sides◦S = 2 circles + middle◦S = 2 (r2) + L*h◦S = 2 ((12)2) + 2(12)*100◦S = 8444.6 m2

Volume◦V = bh = r2*h◦V = (12)2 * 100 = 45238.9 m3

Practice SolutionsPractice Solutions

2 in

5 in

Volunteers?

Volume◦V = 1/3 bh = 1/3 r2 * h◦V = 1/3 22 * 5 = 20.9 in3

Surface area◦S = sum of area of all sides◦S = circle + top◦S = r2 + oops!◦S = r2 + rs◦S = 22 + 2*29◦S = 23.3 in2

S = r2 + rs

r

hs

How do we find s?s2 = r2 + h2

s2 = 22 + 52 = 29s = 29

Practical ApplicationsPractical Applications How would you be able to use this in real life?

◦ Discuss in a small group (3-4) Home Improvement

◦ Figuring out the square footage to know how many materials to get (flooring, paint, etc.)

Short cuts◦ Did you know that the shortest flying distance from

Florida to the Philippine Islands is a path across Alaska?

Object shaping◦ Ex: cutting wood to get the desired shapes when

building furniture

Pool shark◦ Have you ever noticed the angles, measures, and

physics involved in the game of pool?

Career optionsCareer options Computer graphics Virtual reality Biochemical modeling Facial recognition Engineering

◦ Civil◦ Mechanical◦ Computer

Cartography◦ geo sciences◦ construction

Astronomy Contracting Architecture

ArchitectArchitectIf you could build a colony on the

moon, what would you do and why?

What figures and shapes would you use?