Exploring the Geometry of Cones through Surface Area Calculation

Delve into the world of cones by understanding how to calculate the length of the slanted side, the shape of the net to form a cone's curved face, and working out the surface area of a cone using various mathematical concepts and techniques. Explore images and discussions to enhance your understanding of cone geometry.

• Geometry
• Cones
• Surface Area
• Calculations
• Mathematical Concepts

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Uploaded on Oct 10, 2024 | 0 Views

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1. It is common that the slanted edge of a cone is denoted with the letter ?. Discuss: How can we calculate the length of the slanted side given the radius and height of a cone?

2. How can we calculate the length of the slanted side? ?2= 82+ 62 ? ?2= 100 ? = 10 cm

3. On your whiteboards Work out the length of the slanted side

4. On your whiteboards Work out the length of the slanted side

5. On your whiteboards Work out the length of the slanted side

6. Discuss: What shape would the net be to make the curved face of a cone?

7. It is common that the slanted edge of a cone is denoted with the letter ?. The net of the curved surface area of cone is a sector.

8. Discuss: What are the lengths of the sector highlighted in red? On your whiteboards: Write an expression for the area of this sector. 2?? ?

9. 2?? 2?? ??2 ? = 2?? ? ? ? ??2 ? = ? = ???

10. Title: Surface Area of a Cone Your Turn Worked Example Calculate the total surface area of this cone correct to 2 significant figures. Calculate the total surface area of this cone correct to 2 significant figures.

11. Independent Practise Calculate the total surface area. Give your answer to 3 significant figures. 1. 2. 3. 6. 5. 4.

12. Mark/Correct your work . 1. 2. 3. 6. 5. 4.

13. Calculate the curved surface areas of these two cones in terms of pi.

14. How can these surface areas help us calculate the surface area of this FRUSTRUM?

15. Challenge Calculate the surface area of this frustum.