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Estimation of Pi (Grades 11-12)

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Estimation of Pi

1. 
For a circle of radius 1 inscribed in a square, find the perimeter of the square. Then, find the value of the perimeter of the square divided by the diameter of the inscribed circle.




2. 
For a circle of radius 1 inscribed in a regular hexagon, find the perimeter of the hexagon, and the value of the perimeter divided by the diameter of the circle. Calculate all answers to four decimal places.




3. 
For a circle of radius 1 inscribed in a regular decagon, find the perimeter of the decagon, and the value of the perimeter divided by the diameter of the circle. Calculate all answers to four decimal places.




4. 
For a circle of radius 1 inscribed in a regular 40-sided polygon, find the perimeter of the polygon, and the value of the perimeter divided by the diameter of the circle. Calculate all answers to four decimal places.




5. 
Explain how using circumscribed polygons could give an approximation to the value of pi. Would this approximation be an overestimate, underestimate, or neither?




6. 
For a square inscribed in a circle of radius 1, find the perimeter of the square, and the value of the perimeter divided by the diameter of the circumscribed circle.




7. 
For a regular hexagon inscribed in a circle of radius 1, find the perimeter of the hexagon, and the value of the perimeter divided by the radius of the circumscribed circle. Calculate all answers to four decimal places.




8. 
For a regular decagon inscribed in a circle of radius 1, find the perimeter of the decagon, and the value of the perimeter divided by the diameter of the circumscribed circle. Calculate all answers to four decimal places.




9. 
For a regular 40-sided polygon inscribed in a circle of radius 1, find the perimeter of the polygon, and the value of the perimeter divided by the diameter of the circumscribed circle. Calculate all answers to four decimal places.




10. 
Explain how you could give an approximation for pi using inscribed regular polygons. Would this be an overestimate, underestimate, or neither?




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