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Question 3 [35 marks] Write a program called 'pi.py' that calculates the value of PI and then computes and displays the area of a circle with radius entered by the user. PI must be approximated using the following formula. Note that this formula has an infinite number of terms with increasing complexity, so you must multiply additional terms until the size of the next term is 1! $2 imes frac{2}{sqrt{2}} imes frac{2}{sqrt{2 + sqrt{2}}} imes frac{2}{sqrt{2 + sqrt{2 + sqrt{2}}}}$ Hint: This problem requires the use of a 'while' loop to accumulate each term. Also, use the round function to display the computed values with 3 decimal places e.g. round(5.23517, 3) is 5.235. Sample I/O: Approximation of pi: 3.142 Enter the radius: 2.5 Area: 19.635 Submission

          Question 3 [35 marks]
Write a program called 'pi.py' that calculates the value of PI and then computes and displays the
area of a circle with radius entered by the user. PI must be approximated using the following
formula. Note that this formula has an infinite number of terms with increasing complexity, so you
must multiply additional terms until the size of the next term is 1!
$2 	imes frac{2}{sqrt{2}} 	imes frac{2}{sqrt{2 + sqrt{2}}} 	imes frac{2}{sqrt{2 + sqrt{2 + sqrt{2}}}}$
Hint: This problem requires the use of a 'while' loop to accumulate each term. Also, use the
round function to display the computed values with 3 decimal places e.g. round(5.23517, 3)
is 5.235.
Sample I/O:
Approximation of pi: 3.142
Enter the radius:
2.5
Area: 19.635
Submission

$Question 3 [35 marks] Write a program called 'pi.py' that calculates the value of PI and then computes and displays the area of a circle with radius entered by the user. PI must be approximated using the following formula. Note that this formula has an infinite number of terms with increasing complexity, so you must multiply additional terms until the size of the next term is 1! 2 imes frac2sqrt2 imes frac2sqrt2 + sqrt2 imes frac2sqrt2 + sqrt2 + sqrt2 Hint: This problem requires the use of a 'while' loop to accumulate each term. Also, use the round function to display the computed values with 3 decimal places e.g. round(5.23517, 3) is 5.235. Sample I/O: Approximation of pi: 3.142 Enter the radius: 2.5 Area: 19.635 Submission$

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