Group 4- CONES• Boon Yi Chung• Chan Tian Ji• Deong Khai Keat• Kiraly Renaud• Nigel Tan Yong Chien• Ong Chia Hong

CONES

How does a cone forms?

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DEFINITION OF A CONE:

3-dimensional solid object that has :a) circular base,b) one vertex.

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What is Vertex ?

For example, a triangle has 3 vertices.

Vertex a corner :

Calculation of the volume and the area of a cone.

Calculation of a cone

Volume = πr²h

Cone

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Lateral Surface Area = πrs

= πr √ (r² + h²

Total Surface Area = πr² + πrs

= πr² + πr √ r² + h²

For example…

Volume of a cone

== 103.69 cm3

πr²h 31

=

31

31

(3.142) (3)2 (11)

Volume of a cone formula = πr2h

π= 3.142r = 3 cm

h = 11 cm

3 cm

11 cm

What if a cone without vertex?

?

Truncated cone

r

R

S

r

R

S

r

S

R

= radius of upper base

= radius of lower base

= slant height

Truncated cone

h

h = height

Calculation of a truncated cone

πh 3

(r² +rR + R²)Volume=

Lateral Surface Area = π(r + R)S

= π(r + R) √(R - r)²+h²

Total Surface Area = π(r + R)S + π² + πR²

= π(r + R) √(R - r)²+ h² + πr² + πR²

How about….?

-A cone with an vertex that is not aligned above the centre of the base.

DEFINITION OF AN OBLIQUE CONE:

Oblique ConeVertex not aligned

at the centre of the base

Oblique cone

3

r

1

Calculation of an oblique cone

(area of base)(cone height)=

31

= Bh

*B= πr2

For example

r

B= πr231

31 31 31

Volume of oblique cone= Bh

= πr2h

= (3.142) (3)2(9)

Formula of oblique cone = Bh

π = 3.142r = 3 cmH = 9 cm

Given radius of base is 3 cm, height of cone is 9 cm.

Calculate the volume of the oblique cone.

= 84.83 cm3

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Volume of an oblique cone= Bh

Volume of a right cone= πr2 H

B= area of base

πr2 = area of base

B = area of base = πr2

The formulas are SAME !

Conclusion :

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The End