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

2. CONES

3. How does a cone forms?

5. 5
DEFINITION OF A CONE:
3-dimensional solid object that has :
a) circular base,
b) one vertex.

6. 6
What is 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?

12. Truncated cone
r
R
S

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

14. How about….?

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

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

21. The End