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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?
5
DEFINITION OF A CONE:
3-dimensional solid object that has :
a) circular base,
b) one vertex.
6
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
3
1
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
3
1
=
3
1
3
1
(3.142) (3)2 (11)
Volume of a cone formula = πr2h
π= 3.142
r = 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 Cone
Vertex not aligned
at the centre of
the base
Oblique cone
3
r
1
Calculation of an oblique cone
(area of base)(cone height)=
3
1
= Bh
*B= πr2
For example
r
B= πr2
3
1
3
1
3
1
3
1
Volume of oblique cone
= Bh
= πr2h
= (3.142) (3)2(9)
Formula of oblique cone = Bh
π = 3.142
r = 3 cm
H = 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
20
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 :
3
1
3
1
The End

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(Maths) finalize

  • 1. Group 4- CONES • Boon Yi Chung • Chan Tian Ji • Deong Khai Keat • Kiraly Renaud • Nigel Tan Yong Chien • Ong Chia Hong
  • 3. How does a cone forms?
  • 4.
  • 5. 5 DEFINITION OF A CONE: 3-dimensional solid object that has : a) circular base, b) one vertex.
  • 7. For example, a triangle has 3 vertices. Vertex a corner :
  • 8. Calculation of the volume and the area of a cone.
  • 9. Calculation of a cone Volume = πr²h Cone 3 1 Lateral Surface Area = πrs = πr √ (r² + h² Total Surface Area = πr² + πrs = πr² + πr √ r² + h²
  • 10. For example… Volume of a cone = = 103.69 cm3 πr²h 3 1 = 3 1 3 1 (3.142) (3)2 (11) Volume of a cone formula = πr2h π= 3.142 r = 3 cm h = 11 cm 3 cm 11 cm
  • 11. What if a cone without vertex?
  • 13. 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
  • 15. -A cone with an vertex that is not aligned above the centre of the base. DEFINITION OF AN OBLIQUE CONE:
  • 16. Oblique Cone Vertex not aligned at the centre of the base
  • 17.
  • 18. Oblique cone 3 r 1 Calculation of an oblique cone (area of base)(cone height)= 3 1 = Bh *B= πr2
  • 19. For example r B= πr2 3 1 3 1 3 1 3 1 Volume of oblique cone = Bh = πr2h = (3.142) (3)2(9) Formula of oblique cone = Bh π = 3.142 r = 3 cm H = 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
  • 20. 20 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 : 3 1 3 1