Transcript Math Alliance April 26, 2011 Measurement of 3D Figures Process of Measurement Decide on the attribute to be measured Select a unit that has that.

Math Alliance
April 26, 2011
Measurement of 3D
Figures
Process of Measurement
Decide on the attribute to be measured
Select a unit that has that attribute
Fill, cover or match the unit to the
attribute of the object
What is Volume?
Write your own definition.
Develop a table definition.
Volume is the number of cubic units
it takes to fill a solid figure.
How might this be confusing for
students?
Big Ideas for Measuring Volume
Volume is defined by filling.
(The Moving Principle) The volume of a
shape does not depend on its position or
orientation.
(The Combining Principle) Volume is
additive.
Volume of a Rectangular Prism
How would you find the volume of this figure?
How would you explain
this formula to a group of
students?
Volume of a Prism with a Parallelogram Base
How could you use the moving and combining principles
to find the volume of this figure?
Could you change the
shape of the base to
something you know?
So the final formula
would be:
(Area of base) x Height
Volume of a Prism with a Triangular Base
How could you find the volume of this figure?
Could you combine two copies of the figure to give
something you know?
So the final formula would be:
(Area of base) x height
Volume of a Prism with a General Polygon Base
How would you find the volume of this figure?
How can you reduce this problem
to one that you know?
So the final formula would be:
(Area of base) x height
Volume of a Prism with a Circular Base
How would you find the volume of this figure?
How can you relate this
problem to something you
already know?
So the final formula would be:
(Area of base) x height
So, for any prism…
The volume is the area of the
base multiplied by the height.
Investigation
How do you find the volume of
pyramids?
– Would the area of the base multiplied by
the height provide the correct
measurement of a pyramid’s volume?
Why or why not? Discuss.
– Sand/rice demonstration.
Pyramids and Cones
So for pyramids and cones, the volume
is equal to 1/3 of the area of the base of
the figure multiplied by the height
Homework
–Read Section 12.3
–Section 12.3: 1-20, 28, 29,
35, 37, 43, 48, 51, 53
• Turn in: 28, 29, 35, 37, 48