7 april 2011 warm up– silently please 1 ) homework due next class: pg. 524: 1 – 22 just write...

7 April 2011 Warm UP– 7 April 2011 Warm UP– silently pleasesilently please

1) HOMEWORK DUE NEXT CLASS: pg. 524: 1 – 22 just write your answer

2) WARM UP- Silently do handout on 10.1 terms

THINK- 5 minutes independentPAIR- 5 minutes work with partnerSHARE- whole class review

ObjectiveStudents will be able to define the basic vocabulary of

polyhedrons and find the volume of prisms and cylinders.

Homework Due TODAY 10 word cards

Solids WorksheetFind as many similarities and differences between

pairs of figures as you can.Each group will be assigned one row or one

column.Consider symmetry parallelism perpendicularity congruent parts

Volume: Volume: •the measure of the the measure of the amount of space amount of space contained in a solidcontained in a solid• measured in cubic units measured in cubic units (in(in3 3 , ft, ft33))

Volume = Surface Volume = Surface Area Area The sum of the areas The sum of the areas

of all the faceof all the face

The ‘outside’ of the The ‘outside’ of the geometric figuregeometric figure

Use area formulasUse area formulas Measured in square Measured in square inches, square feet…inches, square feet…

The measure of the The measure of the amount of space amount of space

contained in a solidcontained in a solid The ‘inside’ of the The ‘inside’ of the

geometric figuregeometric figure Use volume formulasUse volume formulas measured in cubic measured in cubic feet, cubic inches…feet, cubic inches…

base or side???

base- which part is the base of each object?

sides- which parts are the sides? What type of polygon forms the sides of each?

prisms and cylinders each have TWO CONGRUENT and PARALLEL bases

So……Prism: 2 congruent parallel bases bases are _____________ sides are _____________Cylinder: 2 congruent parallel bases bases are ___________ side “unwrapped” is a _______________Pyramid: one base that is a _____________ sides are ________________Cone: 1 base that is a _____________

Geometric SolidsGeometric Solids 2 Bases2 Bases 1 Base1 Base No BaseNo Base

Prisms & Prisms & CylindersCylinders

Cones & Cones & pyramidspyramids

SpheresSpheres

Bases are congruent and parallel

Right Right PrismPrism

Base

Base

LateralLateraledgeedge

Lateral

Lateral

faceface

heightheight

Oblique CylinderOblique Cylinder

Altitude (segment) = height Altitude (segment) = height (length of segment)(length of segment)

Right Cylinder

Altitude

Think of altitude of a plane--- it is the distance straight down to the ground

Right CylinderRight Cylinder

Oblique Rectangular

Prism

Altitude = heightAltitude = height

altitude is the PERPENDICULAR line segment from a vertex or base to the plane of the opposite base

Term Definition Example

Polyhedron: A solid formed by polygons(polygon-closed figure formed

by line segments)

Faces The flat polygonal surfaces of a polyhedron

Base Two congruent, parallel faces of a prism or cylinder. The

bottom of a pyramid or cone.

Edge

Vertex

The segment where two faces intersect

The point of intersection of three or more edges

TetrahedronHexahedronHeptahedronDecahedrondodecahedro

n

4 sided polyhedron6 sided polyhedron7 sided polyhedron

10 sided polyhedron12 sided polyhedron

l

face

edge

vertex

Name that part….

For your object--- identify its base(s) lateral edges lateral faces vertex / vertices

Review

How can you identify an oblique pyramid from a right pyramid?

Classifying solids3-D objects either have only flat faces or they

have curved faces (all curved or curves mixed with flat surfaces)

POLYHEDRONSFLAT FACES CURVED FACES

ConesCylindersSpheresHemispheres

Prisms Pyramids

thinking about volume

Demonstration- What is the area of the base of the figure?

To fill the space, we can STACK the cubes.

The number of cubes in the bottom layer represents the area of the base.

Investigation, pg. 531--- Find the volume of figures a, b and c.

Term Definition Example

Volume The measure of the amount of space contained in a solid

Measured in cubic units

Prism/cylinder volume

conjecture

The volume of a prism or a cylinder is the area of the

base multiplied by the height

Volume = Areabasex H

Volume

VolumeVolume

6in4in

14in

VOLUME = Area of the BASE x Height of object

What about if it is OBLIQUE??

Demonstration Stack of paper Stack of pennies