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Boon Chung

The document defines different types of cones and provides formulas to calculate their volumes and surface areas. It describes: - A regular cone with a circular base and single vertex point. The volume formula is r^2h and surface area formulas are provided. - A truncated cone which is a cone that has been cut off by two parallel planes. Formulas for volume and surface area are given. - An oblique cone where the vertex is not above the center of the base. The volume formula is the same as a regular cone (Bh) where B is the area of the base. - Examples are provided to demonstrate calculating the volume of different cone types using the formulas.

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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?
(Maths) finalize
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 = r族h Cone 3 1 Lateral Surface Area = rs = r (r族 + h族 Total Surface Area = r族 + rs = r族 + r r族 + h族
For example Volume of a cone = = 103.69 cm3 r族h 3 1 = 3 1 3 1 (3.142) (3)2 (11) Volume of a cone formula = r2h = 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 h 3 (r族 +rR + R族)Volume= Lateral Surface Area = (r + R)S = (r + R) (R - r)族+h族 Total Surface Area = (r + R)S + 族 + R族 = (r + R) (R - r)族+ h族 + r族 + R族
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
(Maths) finalize
Oblique cone 3 r 1 Calculation of an oblique cone (area of base)(cone height)= 3 1 = Bh *B= r2
For example r B= r2 3 1 3 1 3 1 3 1 Volume of oblique cone = Bh = r2h = (3.142) (3)2(9) Formula of oblique cone = Bh = 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 = r2 H B= area of base r2 = area of base B = area of base = r2 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?
  • 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 = r族h Cone 3 1 Lateral Surface Area = rs = r (r族 + h族 Total Surface Area = r族 + rs = r族 + r r族 + h族
  • 10. For example Volume of a cone = = 103.69 cm3 r族h 3 1 = 3 1 3 1 (3.142) (3)2 (11) Volume of a cone formula = r2h = 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 h 3 (r族 +rR + R族)Volume= Lateral Surface Area = (r + R)S = (r + R) (R - r)族+h族 Total Surface Area = (r + R)S + 族 + R族 = (r + R) (R - r)族+ h族 + r族 + R族
  • 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= r2
  • 19. For example r B= r2 3 1 3 1 3 1 3 1 Volume of oblique cone = Bh = r2h = (3.142) (3)2(9) Formula of oblique cone = Bh = 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 = r2 H B= area of base r2 = area of base B = area of base = r2 The formulas are SAME ! Conclusion : 3 1 3 1