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