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Perimeter & Circumference

Directions: Using the digits 1-6, at most one time each, fill in the boxes to create the largest and smallest combined perimeter/circumference for the rectangle and circle.

Hint

Hint

Which box number change has the greatest effect on the combined perimeter/circumference? Why?
What part of your calculations will be the same every time?

How many permutations are there of the numbers 1-6 in four positions?
Which permutations matter for the largest sum? Why?
Which permutations matter for the smallest sum? Why?

Answer

Answer

greatest: (53 · 6) + (2π · 4) = 343.13… units

least: (24 · 1) + (2π · 3) = 42.85… units

Source: Christin Smith

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14 comments

  1. The solution given is actually for area of the rectangle and circumference of the circle

    • Where do you put the numbers? Like which boxes? Thanks.

      • You can choose to use any of the digits 1-6 in each of the boxes so that the rectangle has side lengths and the circle has a radius. You can only use each digit once.

    • David, you are right. With the solution (with given numbers) should look like:
      greatest: (2*53+2*6)+(2π · 4)=143.13….
      least: (2*24+2*1)+(2π · 3)=68.84…..

      HOWEVER: Neither are the greatest or smalles that we found.
      Greatest: (2*65+2*4)+(2π · 3)=156.84…
      Least: (2*13+2*4)+(2π · 2)=46.56…

  2. Greatest: Rectangle with sides 63 and 4 and circle with radius 5. Answer: 165.4

  3. Least: Rectangle with sides 13 and 4 and circle with radius 2. Answer: 46.56

  4. Are we finding the smallest perimeter or area???

  5. My students came up with the following for greatest:

    2(64+3) + (5*2*pi) = 134 + 31.4 = 165.4

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