Surface Area and Volume
Broward County
Teacher Quality Grant
Big Idea 2:
• Develop an understanding of and use formulas
to determine surface areas and volumes of
three-dimensional shapes.
Benchmarks
• MA.7.G.2.1: Justify and apply formulas for
surface area and volume of pyramids, prisms,
cylinders, and cones.
• MA.7.G.2.2: Use formulas to find surface areas
and volume of three-dimensional composite
shapes.
Vocabulary
• The vocabulary can easily
be generated from the
reference sheet and the
Key.
• This will help you not
only to review key
vocabulary but the
symbols for each word.
Vocabulary
• Take out the vocabulary sheet provided for you
and fill in the second column with the definition
for each word.
– Vocabulary Activity Sheet
• Next label the part image in the third column
with the letter representing the corresponding
vocabulary word. If there is no image draw one.
Review Perimeter
• Use the worksheets to review circumference and
Pi
– Rolling a circle
– Archemedes estimation of Pi
• Use the following PowerPoint to review
Perimeter
– Perimeter PowerPoint
Review Topics
GeoGebra activities for Area of Polygons and
Circles
• Rectangles:
– Area of a Rectangle
• Parallelograms:
– Area of a Parallelogram
• Triangles:
– Area of a Triangle
Review Topics
GeoGebra activities for Area of Polygons and
Circles
• Trapezoids:
– Area of a Trapezoid
• Circles:
– Area of a Circles
Review Composite Shapes
• PowerPoint for discussing area and perimeter of
composite figures.
– Composite Shapes PowerPoint
Rectangular Solid
Top
Side 2
Back
Front
Bottom
Side 1
Height (H)
Breadth (B)
Length (L)
GeoGebra for a Cube
Bases
• Do the words Bottom and Base mean the same
thing?
Base of a 3D Figure
• Prism: a prism has 2 Bases and the bases, in all
but a rectangular prism, are the pair of nonrectangular sides. These sides are congruent,
Parallel.
Bases
Triangular Prism
Base of a 3D Figure
Bases
Cylinder
GeoGebra Net for Cylinder
Base of a 3D Figure
• Pyramid: There is 1 Base and the Base is the surface that
is not a triangle.
Base
Base of a 3D Figure
• Pyramid: In the case of a triangular pyramid all sides are
triangles. So the base is typically the side it is resting on,
but any surface could be considered the base.
Base
Net Activity
• Directions sheet
• Net Sheets
• Scissors
• Tape/glue
Building Polyhedra
GeoGebra Nets
• Net of a Cube
• Net of a Square Pyramid
• Net of a Cylinder
• Net of a Cone
• Net of an Octahedron
The net
?
w
?
h
h
?b
h
w
h
b
b
b
w
h
h
h
w
h
b
b
w
Total surface Area
w
h
b
wxh
wxb
bxh
bxh b
h
h
wxh
wxb
b
w
Total surface Area =
+
+
+
+
= 2(b x h) + 2(w x h) + 2(w x b)
= 2(b x h + w x h + w x b)
+
Total surface Area
Nets of a Cube
•
GeoGebra Net of a Cube
Activity: Nets of a Cube
• Given graph paper draw all possible nets for a cube.
• Cube Activity Webpage
Nets of a Cube
Lateral Area
• Lateral Area is the surface area excluding the
base(s).
Net of a Cube
Lateral Area
Lateral Sides
Bases
Lateral Area
Bases
Lateral Surface
Net of a cylinder
Stations Activity
• At each station is the image of a 3D object. Find
the following information:
– Fill in the boxes with the appropriate labels
– Write a formula for your surface area
– Write a formula for the area of the base(s)
– Write a formula for the lateral area
Net handouts and visuals
• Printable nets
– http://www.senteacher.org/wk/3dshape.php
– http://www.korthalsaltes.com/index.html
– http://www.aspexsoftware.com/model_maker_nets_
of_shapes.htm
– http://www.mathsisfun.com/platonic_solids.html
• GeoGebra Nets
– http://www.geogebra.org/en/wiki/index.php/User:K
note
Volume
• The amount of space occupied by any 3dimensional object.
• The number of cubic units needed to fill the
space occupied by a solid
Volume Activity
• Grid paper
• Scissors
• 1 set of cubes
• Tape
Solid 1
Solid 2
Solid 3
Solid 3
Solids 4 & 5
• Circular Base
• Pentagon Base
Volume
• The number of cubic units needed to fill the
space occupied by a solid.
1cm
1cm
1cm
Volume = Base area x height
= 1cm2 x 1cm
= 1cm3
Rectangular Prism
L
L
L
• Volume = Base area x height
= (b x w) x h
=Bxh
• Total surface area = 2(b x w + w x h + bxh)
Comparing Volume
When comparing the volume of a Prism and a Pyramid we focus on
the ones with the same height and congruent bases.
h
h
w
b
Comparing Volume
b
w
h
h
w
w
b
b
Comparing Volume
h
l
Comparing Volume
h
l
Comparing Volume
Prism
Pyramid
Volume = B x h = b x w x h
Volume = 1/3 (B x h) = 1/3 (b x w x h)
h
h
w
w
b
b
Name
Cube
Rectangular
Solid
Figure
Volume
Total
surface
area
S3
6S2
bxwxh
2(LxB + BxH +
LxH)
Sample
net
Volume formulas
• Prism and Cylinder
– V=B x h
• Pyramid and Cone
– V=1/3 (B x h)
Composite figure
12
8
12