Circle Sectors and Perimeters

Aim:

Understand how to read complicated images to work out sector area, arc length (and cone height).

 

How you'll know that you're on track:

Can calculate \( {\text{Sector}_\text{Area}}=\frac{\theta}{360}\times πr^2 \) and \( \text{Arc}=\frac{\theta}{360}\times πr^2 \) , and correctly apply Pythagoras to find the height of a cone.

 

Time Remaining:

Competition: Which cone will give the best area to height ratio?

  • Calculate the missing values for each shape.

  • Separate the paper into its 8 quadrants.

  • Pick one quadrant to complete first.

  • Find the sector area and the arc length.

  • Contribute those results to the class before repeating it for more quadrants.

 

Time Remaining:

Competition: Which cone will give the best area to height ratio?

  • Calculate all sector areas.
  • Together we will sort the papers from smallest to largest and record your number as a sequence (e.g. “12 345 876”).
  • Do the same for arc length.
  •  
  • Calculate the height of the cone this area wold make if rolled up in 3D.
  • Calculate the 'best' ratio of area to that height.
  • Here we must be careful to interpret ‘best ratio’ as meaning “the least area for the greatest height”

 

Time Remaining:

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Poll Bakcup (input code: 42 45 74) :

Feedback: Class Results

Hidden link to the poll dashboard (need to be logged-in as me to view/edit):https://www.mentimeter.com/s/8fe39ce2dc46b1bec09d3d01c59b319f/a254d7ffe01e/edit

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