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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
- 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?
- 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