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:

https://cuckoo.team/jayteach_ea

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:

https://cuckoo.team/jayteach_ea

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:

https://cuckoo.team/jayteach_ea

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Feedback: Class Results

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S3 Circle Sectors and Perimeters

By Jay Teach

Made with Slides.com

S3 Circle Sectors and Perimeters

·# Competition: Which cone will give the best area to height ratio? · ·Calculate the missing values for each shape. (First scaffold with solving a simpler variant) · ·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. · ·Calculate all sector areas. Sort the papers from smallest to largest and record your number as a sequence (e.g. “12 345 876”). [28 651 473] ·Do the same for arc length. [85 671 234] ·Calculate the height of the cone this area wold make if rolled up in 3D. [24 316 758] ·Calculate the ‘best’ ratio of area to height. [85 671 234] ·Here we must be careful to interpret ‘best ratio’ as meaning “the least area for the greatest height” · ·Triangle r /cm ϴ /° Area /cm² L /cm H /cm Area per Height / cm ·1 1.000 90.00 0.785 1.571 0.968 0.811 ·2 0.500 180.00 0.393 1.571 0.433 0.907 ·3 1.000 114.47 0.999 1.998 0.948 1.054 ·4 0.707 180.00 0.785 2.221 0.612 1.283 ·5 1.414 41.41 0.723 1.022 1.405 0.514 ·6 1.000 60.00 0.524 1.047 0.986 0.531 ·7 1.414 45.00 0.785 1.111 1.403 0.560 ·8 1.414 22.50 0.393 0.555 1.411 0.278

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