Transcript Solid Figures - Troup 6

Solid Figures
Gail Sherman 2010
6th Grade Georgia Performance Standards:
M6M3 Students will determine the volume of fundamental solid figures
(right rectangular prisms, cylinders, pyramids, and cones).
M6M4 Students will determine the surface area of solid figures (right
rectangular prisms and cylinders).
Volume
 CRCT Formula Sheet
gives the following
formula for the volume
of all right solid
figures:
V = Bh
 Big B stands for the
area of the base.
 Small b stands for the
base of a plane figure,
like a triangle.
 Very confusing.
Pardon Me?
Volume of a Rectangular Prism
 What is the shape of the BIG B base?
 rectangle
3
 Find the area of B.
 3x10 = 30
 What is the height?
 5
 Final Answer?
 3x10x5 = 150 units³
5
10
Volume of a Cylinder
 What is the shape of B?
4
 circle
 Find the area of B.
 π x 4² = 16
 What is the height?
 9
 Final answer?
 π x 4² x 9 = 144π
9
Volume of a Cone
 This cone & cylinder have the same size bases
and they are the same height. Do they both
hold the same amount of water?
 Which one holds more?
 How much more?
 Let’s experiment…
Volume of a Cone
 You know that cylinder volume = Bh.
 You know a cone is 1/3 the volume of a
cylinder.
 So…Volume of a cone is:
Bh
V
3
Volume of a Cone
 Find the volume of
the cone.
 Radius is 5.
 Height is 4
Bh
V
3
V
 r 2h
3

 52 4 100
3

3
1
 33 
3
Nets
 Draw a net of a cube.
 How many faces?
Surface Area of a Cube
 Let’s name the faces of our cube.






If
Front
Back
Top
Bottom
Left
Right
each side is 3 inches long, find the
surface area.
Add the areas of the 6 faces!







Front is…… 3x3=9
Back is……. 3x3=9
Top is……… 3x3=9
Bottom is… 3x3=9
Left is……… 3x3=9
Right is……. 3x3=9
And the TOTAL is 54 in²
Rectangular Prism
 Just a box.
 Draw a net for this rectangular prism.
2
4
7
How does your net compare?
2
4
7
☺ It’s ok to be different! ☺
Now find the surface area.
.
Surface Area of a Rectangular Prism
.
Front =
Back
=
Top
=
Bottom =
Right =
Left
=
Total =
Rectangular Prism







Front = 4x7=28
Back
= 4x7=28
Top
= 2x7=14
Bottom = 2x7=14
Right = 2x4=8
Left
= 2x4=8
Total = 100 units ²
Do You See Any Shortcuts?
 S.A. =2(lw+lh+wh)
 S.A. = 2wl+2hl+2wh
Cylinders
 Draw a net of a soup can.
Net of a Cylinder
☺ It’s ok to be different! ☺
Find Surface area
 If the soup can is 10 inches tall and
has a radius of 3 inches.
3
10
Hints…
 Look back at your net
 2 circles
 What’s that formula again?
 1 rectangle
 I know the height
 What is the width?
 Add the parts together
Voila!
 πr² gives me area of a circle.
 3.14 x 3 x 3 =
 I have 2 of them, so I’ll multiply that by 2 =
 2πr gives me circumference (width of rectangle)
 2 x 3.14 x 3 x 10 = 188.4
Top =
28.26
Bottom =
28.26
Rectangle = 188.4
TOTAL =
244.92 in²
Answering With Pi
 Sometimes there is no need to compute pi,
because they want the answer to be precise
and contain pi.
 In that case:
 πr² = π x 3² = 9π
 2πr = 2 x π x 3 x 10 = 60π
 9π + 9π + 60π = 78π