1 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.

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

http://www.mrperezonlinemathtutor.com/

3


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


1 cm 3 10 cm3100 cm3

1000 cm 3

BASE 10 BLOCKS VALUES FOR VOLUMES:


5


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


6 cm 2 42 cm2240 cm2

600 cm 2

BASE 10 BLOCKS VALUES FOR AREAS:


7


FIND THE VOLUME FOR THE FIGURE BELOW:

1000 cu

1000 cu 1000 cu

Total Volume = 3(1000 cu)

= 3000 cu


10

10

10

Volume:

V = Bh

V = (10x10)x10

V = 100x10



8


FIND THE SURFACE AREA FOR THE FIGURE BELOW:


9

x

y

zPRESENTATION CREATED BY SIMON PEREZ. All rights reserved


10


Right and Left Views

x

y

z


11


Top and Bottom Views

x

y

z


12


Front and Back Views

x

y

z


13


ALL Views

x

y

z


14


ALL Views

x

y

z


15


Total Surface Area =

100

100

100

100 100

100

2(300)

x

y

z


16



100

100 100

100

2(200)

x

z

y


17



100 100

100 100

2(200)

x

z

y


18



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


FRONT VIEW

RIGHT VIEW

TOP VIEW

Eliminating redundant views draw an orthographic drawing of the previous figure:


20


Now draw an isometric drawing of the figure (corner view):


21


Draw a FOUNDATION drawing of the ISOMETRIC figure:

FOUNDATION DRAWING

2 1

Indicates 2 levels

Indicates 1 level

Using the top view:


22




10

10

10

Volume:

V = Bh

V = (10x10)x10

V = 100x10


Total Volume =


23




10

10

10

Volume:

V = Bh

V = (10x10)x10

V = 100x10


Total Volume =

1000 cu

1000 cu

1000 cu


= 4000 cu

1000 cu


24




10

10

10

Volume:

V = Bh

V = (10x10)x10

V = 100x10



= 4000 cu


25


FIND THE SURFACE AREA FOR THE FIGURE BELOW:


26

x

y

zPRESENTATION CREATED BY SIMON PEREZ. All rights reserved


27


Right and Left Views

x

y

z


28


Top and Bottom Views

x

y

z


29


Front and Back Views

x

y

z


30


ALL Views

x

y

z


31


ALL Views

x

y

z


32


x

y

z


100

100

100

100 100

100

2(300)


33


x

y

z

Total Surface Area = 2(300)

100

100

100

100

100

100


34


x

y

z

Total Surface Area = 2(300)

100 100

100

100 100

100


35


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


Eliminating redundant views draw an orthographic drawing of the previous figure:

FRONT VIEW

RIGHT VIEW

TOP VIEW


37


Now draw an isometric drawing of the figure:


38


FOUNDATION DRAWING

Draw a FOUNDATION drawing of the ISOMETRIC figure:

2 1

Indicates 2 levels

Using the top view:

1 Indicates 1 level


39


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


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


TOP VIEW

FRONT VIEW

RIGHT VIEW

200

60 262

2

400

40440

400

800

524

880


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


Build the figure represented in the orthographic views below:

TOP VIEW

FRONT VIEW

RIGHT VIEW


43


FRONT RIGHT

Draw an isometric drawing of the figure:


44


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.



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


1 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.

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