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Contents

1. Title : Sculpture for the Mathematics Corner of SMK Muar. page 1

2. Appreciations : page 3

3. Introductions: page 4

4. Materials and Techniques : page 5

5. Examples of Chinese Sculptures: page 6

6. Examples of Japanese Sculptures: page 7

7. Examples of Sculptures from Central Asia: page 8

8. Task Specifications: page 9

9. Problem solving: page 10

10. Results Obtained : page 15

11. Reflections : Page 18

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2.Appreciations :

I would like to thank my Additional Mathematics teacher ………………………………………

for explaining to us and guide us throughout this project work. Without him/her , I wouldn’t have able to

do this project so smoothly.

I would also like to take this opportunity to thank my friends ………………………………… for all their 

cooperation in doing the project together and obtaining the results.

Lastly I would like to thank my parents for their moral and financial support .

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3.Introduction

Sculpture is three-dimensional artwork created by shaping or combining hard materials —typicallystone such as marble—or metal, glass, or wood except when softer ("plastic") materials can also beused, such as clay, textiles, plastics, polymers and softer metals or when the term has been extendedto works including sound, text and light.

Materials may be worked by removal such as carving; or they may be assembled such as by welding, hardened such as by firing, or molded or cast. Surface decoration such as paint may be applied .Sculpture has been described as one of the plastic arts because it can involve the use of materials thatcan be moulded or modulated. Found objects may be presented as sculptures.

Sculpture is an important form of public art. A collection of sculpture in a garden setting may be referredto as a sculpture garden. 

Some common forms of sculpture are :

  Free-standing sculpture, sculpture that is surrounded on all sides, except the base, by space. Itis also known as sculpture "in the round", and is meant to be viewed from any angle.  Sound sculpture  Light sculpture  Jewellery or Jewelry  Relief – the sculpture is attached to a background; types are bas-relief, alto-relievo, and sunken-

relief  Site-specific art  Kinetic sculpture – involves aspects of physical motion

o  Fountain – the sculpture is designed with moving watero  Mobile

  Statue – representationalist sculpture depicting a specific entity, usually a person, event, animal

or objecto  Bust – representation of a person from the chest upo  Equestrian statue – typically showing a significant person on horseback

  Stacked art – a form of sculpture formed by assembling objects and 'stacking' them  Architectural sculpture  Environmental art

o  Environmental sculptureo  Land art

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4 Materials and techniques

The materials used in sculpture are diverse, changing throughout history. Sculptors have generallysought to produce works of art that are as permanent as possible, working in durable and frequentlyexpensive materials such as bronze and stone: marble, limestone, porphyry, and granite. More rarely,precious materials such as gold, silver, jade, and ivory were used for chryselephantine works. More

common and less expensive materials were used for sculpture for wider consumption, including glass, hardwoods (such as oak, box/boxwood, and lime/linden); terracotta and other ceramics, and castmetals such as pewter and zinc (spelter).

Sculptures are often painted, but commonly lose their paint to time, or restorers. Many different paintingtechniques have been used in making sculpture, including tempera, [oil painting], gilding, house paint,aerosol, enamel and sandblasting.

Many sculptors seek new ways and materials to make art. One of Pablo Picasso's most famoussculptures included bicycle parts. Alexander Calder and other modernists made spectacular use ofpainted steel. Since the 1960s, acrylics and other plastics have been used as well. Andy Goldsworthymakes his unusually ephemeral sculptures from almost entirely natural materials in natural settings.Some sculpture, such as ice sculpture, sand sculpture, and gas sculpture, is deliberately short-lived. Avast array of sculptors including Joan Miró, Marcel Duchamp, Yves Klein, John Chamberlain, JeanTinguely, Richard Stankiewicz, Larry Bell, Carl Andre, Louise Bourgeois and others used glass, stainedglass, automobile parts, tools, machine parts, and hardware to fashion their works.

Sculptors often build small preliminary works called maquettes of ephemeral materials such as plasterof Paris, wax, clay, or plasticine, as Alfred Gilbert did for 'Eros' at Piccadilly Circus, London. InRetroarchaeology, these materials are generally the end product.

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5.Examples of Chinese Sculptures

A Liao Dynasty polychrome wood-carved statueof Guan Yin, Shanxi Province, China, (907 –1125AD)

Wine jar, Western Zhou Dynasty (1050 BC-771BC)

Calvalryman, Qin Dynasty

Chimera (from a tomb) , Han Dynasty (202 BC-220 AD)

Seated Buddha, Tang Dynasty ca. 650.Boddisatva, Tang Dynasty (618 –907)

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6.Example of Japanese Sculptures

The Great Buddha of Kamakura, c. 1252, Japan

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7. Examples of sculptures from Central Asia

Sumerian male worshiper, 2750-2600 B.C.

Fragment of the wind god Boreas, Hadda, Afghanistan

Gandharan Atalante. 

Gandhara Poseidon (Ancient OrientMuseum) 

A Nepalese polychrome wooden statue of theMalla Kingdom, 14th century

13th century Ganesha

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8.Task Specifications :

Part A

(a) Based on different reference points, find at least three different functions that can represent

the curve of the concrete structure.(b) Find the area of the front surface of the structure.

Part B

Given four choice of the concrete structure :-

(a) Determine the structure that will give minimum cost . ( Given 1 m3 of concrete is RM 960.00 )(b) Choose the shape of the structure to be built. Give your reasons.

Part C

E

F

D

A

X cm

80 cm

Based on the logo designed by the Mathematics Society:-

(a) Given the area of BDEF is y cm2 , express y in terms of x,

(b) Reduce the non-linear equation in (a) to linear equation . Plot a straight line graph. Determine

the area of BDEF if the length of AB is 5.5 cm,

(c) Determine the maximum area of BDEF using two different methods.

.

BC

D

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9.Problem Solving

PART A

(a) (i)

(ii)

(iii)

(50, -75)(-50, -75)

y = a x2

substitute (50, -75) into the equation

-75 = a(50)2

a= - 0.03

therefore y = - 0.03 x2

y = a x2 + 75

substitute (50, 0) into the equation

0 = a(50)2 + 75

a= - 0.03

therefore y = - 0.03 x2 +75

y = a (x-50)2 + 75

substitute (0, 0) into the equation

0 = a(-50)2 + 75

a= - 0.03

therefore y = - 0.03 ( x-50)2 +75

(50,75)

(100, 0)(0, 0)

(0, 75)

(50, 0)0)

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(b)

100 cm

100 cm

50

2

0

503

0

2

Area 2 ( 0.03 75)

0.032 75

3

5000

 x dx

 x x

cm

 

Area of square base

= 100 x 100

= 10,000 cm2

(0, 75)

(50, 0)0, 0)

Area of parabolic shape on top

Hence total area of the front surface

= 10,000 cm2 + 5, 000 cm2

= 15, 000 cm2

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Choice ( iii) 60 cm

75cm

100cm

100 cm

Choice ( iv) 20 cm

100cm

100cm

Area of the front surface

= 100 x 100 + ½ ( 60 + 100 ) x 75

=16, 000 cm2

Thickness = 13 cm

Volume of concrete used

= 16,000 x 13 = 208, 000 cm3

= 0.208 m3 

1 m3 of concrete cost RM 960.00

Cost of making the sculpture

= 0.208 x 960

= RM 199.68

Area of the front surface

= 100 x 100 + ½ ( 20 + 100 ) x 75

=14 , 500 cm2

Thickness = 13 cm

Volume of concrete used

= 14,500 x 13 = 188, 500 cm3

= 0.1885 m3 

1 m3 of concrete cost RM 960.00

Cost of making the sculpture

= 0.1885 x 960

= RM 180.96

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10.Results obtained

Shape Cost Comments

RM 187.20 Artistic

RM 171.60 Minimum Cost

RM 199.60

RM 180.96

(b) The concrete structure is going to be a permanent structure in the school. Besides considering the

cost of making it, we have to make sure it is nice to the eyes and artistic. After considering all these ,

my choice is (i). I have also consider to make the structure in (i) , we have to make the mould for the

curve top and this will add additional cost. Still I will chose (i)

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Part © 

m

X cm

X cm

(80 - x)

 Area of Δ ACE 

= ½ x 80 x 80 sin 60

= 2771.28 cm2

 Area of Δ ABD 

= ½ x x  x x  sin 60

= 0.866 x2

 Area of Δ BCF 

= ½ x (80- x) x (80- x) sin 60

= 2771.28 – 69.28 x + 0.433 x2

Area of BDEF= y2

2771.28 = 0.866 x2 + 2771.28 – 69.28 x + 0.433 x 2 + y

y = 69.282 x - 1.299 x2

E

A C60

0

80cm 80cm

80cm

A B

D

600

600

B C

F

E

D F

B

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(b) 1.299 69.282 y

 x x

 

x 0 10 20 30 40 50y/x 69.282 56.292 43.302 30.312 17.322 4.332

When x = 5.5 , from graph y/x = 62.5

Hence y = 62.5 x 5.5 = 343.75

 © 2

69.282 1.299 y x x  

Method 1- Calculus Method

2

2

2

max

2

69.282 2.598 0

26.667

2.598(max.)

69.282(26.667) 1.299(26.667)

923.787

dy x

dx

 x

d y

dx y

cm

 

Method 2  – Completing Square Method

2

2

2

2

69.282 1.299

1.299( 53.335 )

1.299 ( 26.667) 711.152

1.299( 26.667) 923.787

 y x x

 x x

 x

 x

 

When x= 26.667 y max= 923.787 cm2

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11. Reflection

The values I learn from doing this project include:

(a) Learn to work as a team,

(b) Must be patient to obtain all the results,(c) Dare to try different methods,

(d) Dare to confront difficult problems,

(e) Importance of accuracy,

(f) Contribute to the school that educate me.