Post on 14-Dec-2015
11
SURFACE AREA
and
VOLUME
with
BASE 10 BLOCKS
INTRODUCTION
PROBLEM 1
PROBLEM 2
PROBLEM 3
PROBLEM 4
PROBLEM 5
PROBLEM 6
PROBLEM 7
PROBLEM 8
PROBLEM 9
2
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
1 cm 3
1000 cm 3
10 cm3100 cm3
3
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
BASE 10 BLOCKS VALUES FOR VOLUMES USING PRISM VOLUME FORMULA:
Volume for each individual Base 10 Block
10
10
10
Volume:
V = Bh
V = (10x10)x10
V = 100x10
V = 1000 cubic units
1010
Volume:
V = Bh
V = (10x10)x1
V = 100x1
V = 100 cubic units
1
1
10
Volume:
V = Bh
V = (1x10)x1
V = 10x1
V = 10 cubic units
1
1 1
Volume:
V = Bh
V = (1x1)x1
V = 1x1
V = 1 cubic units
1
4
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
1 cm 3 10 cm3100 cm3
1000 cm 3
BASE 10 BLOCKS VALUES FOR VOLUMES:
5
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
6 cm 2
42 cm2
240 cm2
600 cm 2
BASE 10 BLOCKS VALUES FOR AREAS:
10x10
6(10x10)
6(100)
Each PRISM has 6 faces
2(10x10)
4(10X1)
2(10x10)+4(10x1)
2(100)+4(10)
200+40
4(10X1)2(1X1)
2(1x1)+4(10x1)
2(1)+4(10)
2+40
6(1X1)
6
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
6 cm 2 42 cm2240 cm2
600 cm 2
BASE 10 BLOCKS VALUES FOR AREAS:
7
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE VOLUME FOR THE FIGURE BELOW:
1000 cu
1000 cu 1000 cu
Total Volume = 3(1000 cu)
= 3000 cu
Volume for each individual Base 10 Block
10
10
10
Volume:
V = Bh
V = (10x10)x10
V = 100x10
V = 1000 cubic units
8
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE SURFACE AREA FOR THE FIGURE BELOW:
9
x
y
zPRESENTATION CREATED BY SIMON PEREZ. All rights reserved
10
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Right and Left Views
x
y
z
11
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Top and Bottom Views
x
y
z
12
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Front and Back Views
x
y
z
13
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
ALL Views
x
y
z
14
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
ALL Views
x
y
z
15
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Total Surface Area =
100
100
100
100 100
100
2(300)
x
y
z
16
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Total Surface Area =
100
100 100
100
2(200)
x
z
y
17
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Total Surface Area =
100 100
100 100
2(200)
x
z
y
18
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Total Surface Area =
100
100
100
100
100
100 100
100
100
100
100 100
100 100
2(300) + 2(200) + 2(200) = 600 + 400 + 400 = 1400 U 2
x
y
z
19
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FRONT VIEW
RIGHT VIEW
TOP VIEW
Eliminating redundant views draw an orthographic drawing of the previous figure:
20
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Now draw an isometric drawing of the figure (corner view):
21
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Draw a FOUNDATION drawing of the ISOMETRIC figure:
FOUNDATION DRAWING
2 1
Indicates 2 levels
Indicates 1 level
Using the top view:
22
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE VOLUME FOR THE FIGURE BELOW:
Volume for each individual Base 10 Block
10
10
10
Volume:
V = Bh
V = (10x10)x10
V = 100x10
V = 1000 cubic units
Total Volume =
23
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE VOLUME FOR THE FIGURE BELOW:
Volume for each individual Base 10 Block
10
10
10
Volume:
V = Bh
V = (10x10)x10
V = 100x10
V = 1000 cubic units
Total Volume =
1000 cu
1000 cu
1000 cu
Total Volume = 4(1000 cu)
= 4000 cu
1000 cu
24
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE VOLUME FOR THE FIGURE BELOW:
Volume for each individual Base 10 Block
10
10
10
Volume:
V = Bh
V = (10x10)x10
V = 100x10
V = 1000 cubic units
Total Volume = 4(1000 cu)
= 4000 cu
25
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FIND THE SURFACE AREA FOR THE FIGURE BELOW:
26
x
y
zPRESENTATION CREATED BY SIMON PEREZ. All rights reserved
27
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Right and Left Views
x
y
z
28
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Top and Bottom Views
x
y
z
29
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Front and Back Views
x
y
z
30
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
ALL Views
x
y
z
31
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
ALL Views
x
y
z
32
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
x
y
z
Total Surface Area =
100
100
100
100 100
100
2(300)
33
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
x
y
z
Total Surface Area = 2(300)
100
100
100
100
100
100
34
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
x
y
z
Total Surface Area = 2(300)
100 100
100
100 100
100
35
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
x
z
100 100
100
100 100
100
Total Surface Area = 2(300) + 2(300) + 2(300) = 600 + 600 + 600 = 1800 U 2
y
100
100
100
100
100
100
100 100
100
100
100
100
36
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Eliminating redundant views draw an orthographic drawing of the previous figure:
FRONT VIEW
RIGHT VIEW
TOP VIEW
37
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Now draw an isometric drawing of the figure:
38
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FOUNDATION DRAWING
Draw a FOUNDATION drawing of the ISOMETRIC figure:
2 1
Indicates 2 levels
Using the top view:
1 Indicates 1 level
39
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Find the volume for the shape below:
1000 c.u.
1000 c.u.
1000 c.u.
1000 c.u.
100 c.u.
100 c.u.
100 c.u.
100 c.u.
100 c.u.
100 c.u.
10 c.
u
10 c.
u
4x 1000
6x 100
2x 10
4000
600
20
4620
VOLUME = 4620 c.u.
40
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
TOP VIEW
FRONT VIEW
RIGHT VIEW
200
60 262
2
400
40440
400
800
524
880
Surface Area =524 + 880 + 800 = 2204 square units
Find the total surface area for the shape below:
100 sq. u.
100 sq. u.
100 sq. u. 100 sq. u.
100 sq. u. 100 sq. u. 100 sq. u.
100 sq. u.
40 sq. u.
30 sq. u.
100 sq. u.
100 sq. u.
2 sq. u.
30 sq. u.
x 2
Top
an
d B
otto
m
x 2
Fron
t an
d B
ack
x 2
Rig
ht
and
Lef
t
41
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
TOP VIEW
FRONT VIEW
RIGHT VIEW
200
60 262
2
400
40440
400
800
524
880
Surface Area =524 + 880 + 800 = 2204 square units
Find the total surface area for the shape below:
x 2
Top
an
d B
otto
m
x 2
Fron
t an
d B
ack
x 2
Rig
ht
and
Lef
t
42
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Build the figure represented in the orthographic views below:
TOP VIEW
FRONT VIEW
RIGHT VIEW
43
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
FRONT RIGHT
Draw an isometric drawing of the figure:
44
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Draw an orthographic drawing of the figure:
TOP VIEW
FRONT VIEW
RIGHT VIEW
45PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Find the surface area:
TOP VIEW
FRONT VIEW
RIGHT VIEW 100 sq. u.
100 sq. u.
100 sq. u.
100 sq. u.
100 sq. u.
500
1000
x 2
Top
an
d B
otto
m
100 sq. u.100 sq. u.
100 sq. u.
100 sq. u.400
800x 2
Rig
ht
and
Lef
t
300
600
x 2
Fron
t an
d B
ack
100 sq. u.
100 sq. u.
100 sq. u.
Surface Area =1000 + 800 + 600 = 2400 square units
46PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Find the surface area:
TOP VIEW
FRONT VIEW
RIGHT VIEW
500
1000
x 2
Top
an
d B
otto
m
400
800x 2
Rig
ht
and
Lef
t
300
600
x 2
Fron
t an
d B
ack
Surface Area =1000 + 800 + 600 = 2400 square units