(Maths) finalize
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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 πr^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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1) Volume of sphere = (4/3)Ï€r^3
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2) Original volume = (4/3)Ï€(10)^3 = 4188 cm^3
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Dr. Lim Yeow Beng is the Principal of T.Y. LININTERNATIONAL SDN BHD, a civil and structural engineering firm in Malaysia. He has over 28 years of experience and holds a PhD from the University of Illinois. As Principal, he oversees projects and ensures designs are safe. Some of the firm's notable projects include Regency Condominium, G Hotel in Penang, and Nu Sentral Mall in Kuala Lumpur. The document provides background on Dr. Lim and details some of the firm's projects he was involved in as Project Manager or Principal. It also includes an organizational chart and advice Dr. Lim gives to future civil and structural engineers.Structuralengeeniring63 141128233958-conversion-gate02-141211073958-conversio...
Structuralengeeniring63 141128233958-conversion-gate02-141211073958-conversio...Boon Chung
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A structural engineer designs and selects materials to build the framework of structures, making them stable, durable, and safe. They analyze how components will bend, compress, or stretch. Throughout a project, a structural engineer will consult with clients, investigate site conditions, calculate loads, decide on structural systems, supervise construction, and ensure safety upon completion. They produce drawings showing reinforcement details and make revisions to account for unexpected issues during construction. The goal is to develop the most suitable structural design and construction process.(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