TAKS Measurement by mikeholy

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```									TAKS: Measurement & 3-D
• 8.7.D: Locate and name points on a coordinate plane
using ordered pairs of rational numbers.
• 8.8.A: Find surface area of prisms and cylinders using
[concrete] models and nets (2-D models).
• 8.8.B: Connect models to formulas for volume of
prisms, cylinders, pyramids, and cones.
• 8.8.C: Estimate answers and use formulas to solve
application problems involving surface area and
volume.
• 8.10.B: Describe the resulting effect on volume when
dimensions of a solid are changed proportionally.
Points on a Coordinate Plane
A coordinate grid
is used to
locate and
name points on
a plane.
Points on a Coordinate Plane
The x-axis
and y-axis
divide the
coordinate
plane into
four
regions,
called
Example
Example
Polyhedron
A solid formed by polygons that enclose a
single region of space is called a
polyhedron.

Separate your Geosolids into 2 groups: Polyhedra and others.
Parts of Polyhedrons
• Polygonal region = face
• Intersection of 2 faces = edge
• Intersection of 3+ edges = vertex

face          edge           vertex
Example
Separate your Geosolid polyhedra into two
groups where each of the groups have
similar characteristics.
These are the only kind of polyhedra on the
TAKS test. What are the names of these
groups?
Prism
A polyhedron is a prism iff it has two
congruent parallel bases and its lateral
faces are parallelograms.
Classification of Prisms
Prisms are classified by their bases.
Right & Oblique Prisms
Prisms can be right or oblique. What
differentiates the two?
Example
Pyramid
A polyhedron is a pyramid iff it has one base
and its lateral faces are triangles with a
common vertex.
Classification of Pyramids
Pyramids are also classified by their bases.
Example
The three-dimensional figure formed by
spinning a two dimensional figure around
an axis is called a solid of revolution.
Cylinder
A cylinder is a 3-D
figure with two
congruent and
parallel circular
bases.
base
• Axis = segment
connecting centers
of bases
Cone
A cone is a 3-D figure
with one circular base
and a vertex not on the
same plane as the base.
• Altitude =
perpendicular segment
connecting vertex to the
plane containing the
base (length = height)
Sphere
A sphere is the set
of all points in
space at a fixed
distance from a
given point.
• Radius = fixed
distance
• Center = given
point
Sections
When a solid is cut by a plane, the resulting
plane figure is called a section. A section
that is parallel to the base is a cross-
section.
Example
Example
Nets
Imagine cutting a 3-D
solid along its
edges and laying
flat all of its
surfaces. This 2-D
figure is a net for
that 3-D solid.
Example
Match one of the red, rubbery nets with its
corresponding 3-D solid. Which of the
shapes has no net?
Example
There are generally two types of
measurements associated with 3-D solids:
surface area and volume. Which of these
can be easily found using a shape’s net?
Surface Area
The surface area of a 3-D
figure is the sum of the
areas of all the faces or
surfaces that enclose the
solid.
• Asking how much
surface area a figure has
is like asking how much
wrapping paper it takes
to cover it.
Lateral Surface Area
The lateral surface area of
a 3-D figure is the sum
of the areas of all the
lateral faces of the solid.
• Think of the lateral
surface area as the size
of a label that you could
put on the figure.
Example
The net can be
folded to form
a cylinder.
What is the
approximate
total surface
area of the
cylinder?
Example
Using the Formula Chart
You could just as easily compute the surface
area using a formula.
Height vs. Slant Height
On the formula chart, h represents height
and l represents slant height.
Height vs. Slant Height
On the formula chart, h represents height
and l represents slant height.
Example
Find the total surface
area of the square
pyramid.
Volume
Volume is the measure
of the amount of
space contained in a
solid, measured in
cubic units.
– This is simply the
number of unit cubes
that can be arranged
to completely fill the
space within a figure.
Example
Find the volume of
the given figure in
cubic units.
More Formulas!
The volume of a solid is also easily
computed with a formula.

What does the B represent?
Example
Example
Example
Which solid has the greater
volume: a cylinder 3 inches
high with a radius of 2
inches or a cone of the
same radius that is 8.5
inches high?
Example
A pipe in the shape of a
cylinder with a 30-inch
diameter is to go through
a passageway shaped
like a rectangular prism.
The passageway is 3 ft
high, 4 ft wide, and 6 ft
long. The space around
the pipe is to be filled with
insulating material.
Example 10
What is the volume of the
insulating material?
Example
Find the volume of a
cube with a side
length of 2 inches.
Now find the volume
of a cube with a
side length of 4
inches.
How do the volumes
compare?
Example
Find the volume of a
cube with a side
length of 2 inches.
Now find the volume
of a cube with a
side length of 4
inches.
How do the volumes
compare?
Volumes of Similar Figures
If two solids have a
scale factor of a:b,
then the
corresponding
volumes have a
ratio of a3:b3.
Similarity Relationships
For two shapes with a scale factor of a:b, each of the
following relationships will be true.
Example
Example
Example
A breakfast-cereal manufacturer is using a
scale factor of 2.5 to increase the size of
one of its cereal boxes. If the volume of the
original cereal box was 240 in.3, what is the
volume of the enlarged box?
Assignment
10th TAKS Practice
Workbook:
• P. 85, 97, 99, 101,
107

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