Volume Given Area of the Base notes
Volume Given
Area of the Base
8th Grade Math
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Volume Given Area of the Base notes
TEKS for the Day
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Volume Given Area of the Base notes
Essential Question(s)
• How are the mathematical formulas used and manipulated to solve geometric problems?
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Volume Given Area of the Base notes
Let's watch a video on Volume!!!
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Volume Given Area of the Base notes
New Vocabulary
Volume
The amount of space inside a three­dimensional object, or its capacity It's units are always "cubic", that is, the number of little element cubes that fit inside the figure. Pyramid
A polyhedron with a base that is a polygon and triangular faces that form a vertex
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Volume Given Area of the Base notes
Student Notes ­ Volume Given Area of the Base
1.
Look at your reference material and determine what volume formula you would use for the
following shapes.
V= Bh
V= Bh
V= Bh
V= Bh
Rectangular Prism: _____________
Cylinder:_______________
Triangular Prism:______________
Cube:_____________
1
V = 3 Bh
Rectangular Pyramid:______________
1
V = 3 Bh
Cone:______________
1
V
=
Bh
3
Triangular Pyramid:________________
1
V = 3 Bh
Square Pyramid:_______________
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Volume Given Area of the Base notes
2. What are the similarities and differences from the list above?
Both shapes are 3­dimensional solids, have
bases and faces.
3. What is the relationship between a prism and pyramid with the same
base and height?
Video ­ Deriving the Formula "Volume of Pyramid"
The volume of the prism is 3 times larger than
the volume of the pyramid.
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The volume of the pyramid is
of the volume
3
of the prism.
4. Is this the same relationship between and cylinder and
cone?
Video ­ Deriving the Formula "Volume of Cone"
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Volume Given Area of the Base notes
Try it!!!
Work problem #5­10 with a Partner
Using that knowledge determine the volume of the figures shown
below.
5.
Square Pyramid
Name:_______________________
1
V
=
Bh
3
Formula: __________________
Equation:_____________________
V = 45 in
3
Volume:__________________
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Volume Given Area of the Base notes
6.
Triangular Prism
Name:_______________________
V= Bh
Formula: __________________
Equation:_____________________
V = 0.48 m
3
Volume:__________________
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Volume Given Area of the Base notes
7.
Area of the base is 24 cm 2.
Triangular Pyramid
Name:_______________________
1
V
=
Bh
3
Formula: __________________
Equation:_____________________
V = 88 cm
3
Volume:__________________
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Volume Given Area of the Base notes
8.
Cone
Name:_______________________
1
V
=
Bh
3
Formula: __________________
Equation:_____________________
V = 25.12 in
Volume:__________________
3
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Volume Given Area of the Base notes
9. If the volume of a cylinder is 1695.6 cm 3, what would be the
volume of a cone with the same dimensions?
V=
1
3
Bh or V = (Bh) ÷ 3
V=
1695.6
3
V = 565.2 cm3
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Volume Given Area of the Base notes
10. If the volume of ice cream cone is 94.2 cm 3, what would be the
volume of cylinder with the same dimensions.
Volume of Cylinder = Volume of Cones
.
.3
V = 94.2 3
V = 282.6 cm3
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Volume Given Area of the Base notes
For the next two shapes the volume is given and you must
determine what would be the area of the base.
11. The volume of the figure below is 18.56 in 3,
V= Bh
Cylinder
Name:_______________________
B = V ÷h
Formula: __________________
Equation:_____________________
V = 6.19 in
Area of the base:_____________
2
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Volume Given Area of the Base notes
12. The volume of the figure below is 110 mm3 and the height is 5.5 mm.
Hexagonal Prism
Name:_______________________
1
V = 3 Bh
Formula: __________________
.
1
B =
or
110
=
B
5.5
3
Equation:_____________________
3(110)
5.5
B = 60 mm2
Area of the base:_____________
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Volume Given Area of the Base notes
Exit Ticket:
Let’s Write About It:
1. How do you find the volume of prism, pyramids, cylinders, and cones?
2. What is the relationship between the volume of a cone and cylinder with
the same dimensions?
Let’s Write About It:
1.
How do you find the volume of prism, pyramids, cylinders, and cones? ______________________________________________________________________________________________
______________________________________________________________________________________________
______________________________________________________________________________________________
______________________________________________________________________________________________
1.
2. is the relationship between the volume of a cone and cylinder with the same dimensions? 16