Finding the volume of a cone.doc - Finding the volume of a cone Step 1 – recapping a 2-D method Use the trapezium rule with strips of height h = 1 cm

# Finding the volume of a cone.doc - Finding the volume of a...

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Finding the volume of a cone Step 1 – recapping a 2-D method Use the trapezium rule with strips of height h = 1 cm to estimate the area of this triangle: Improve your estimate by using strips of height h = 0.5 cm and then h = 0.2 cm. What is the actual area of the triangle? What can you say about your successive estimates? Step 2 – extending the method to 3-D The triangle has now been rotated around the x axis to form a cone. What 3-D shape are your ‘strips’? It may help to visualise a child’s toy with rings of decreasing size on a peg. Use discs of height δx = 1 cm to estimate the volume of the cone. Repeat for discs of height δx = 0.5 cm and δx = 0.2 cm. Use a spreadsheet to predict the actual volume of the cone. Is this what you expected? Repeat for a cone with a different height and base radius. 10 5 x y 10 5 x y
Step 3 – generalising Find the volume of the disc which starts x units from the vertex and has height δx, and of the next disc.

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• Fall '17
• William Heywood

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