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?
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Calculate the missing values for each shape.
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Separate the paper into its 8 quadrants.
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Pick one quadrant to complete first.
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Find the sector area and the arc length.
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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