SOLUTION: The Rhind Mathematical Papyrus, an Egyptian document dating from circa 1650 BC, states that the area of a circular field of diameter 9 units is equal to the area of a square with a

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Question 1199779: The Rhind Mathematical Papyrus, an Egyptian document dating from circa 1650 BC, states that the area of a circular field of diameter 9 units is equal to the area of a square with a side of 8 units. This sets the ancient Egyptian value of π (pi) at
a) 3
b) 3 1/8
c) 3 1/9
d) 3 9/64
e) 3 13/81
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
The Rhind Mathematical Papyrus, an Egyptian document dating from circa 1650 BC, states that the area of a circular field of diameter 9 units is equal to the area of a square with a side of 8 units. This sets the ancient Egyptian value of π (pi) at
a) 3
b) 3 1/8
c) 3 1/9
d) 3 9/64
e) 3 13/81
a = pi* r^2
when d = 9, r = 4.5
the area of a square with a side of 8 units is equa to 8^2 = 64
you get:
64 = pi * 4.5^2
solve for pi to get:
64 / 4.5^2 = pi = 3.160493827
1/8 = .125
1/9 = .11111.....
9/64 = .140625
13/81 = .1604938272
looks like selection e is the answer.
3 + 13/81 = 3.160493827.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
The Rhind Mathematical Papyrus, an Egyptian document dating from circa 1650 BC,
states that the area of a circular field of diameter 9 units is equal to the area
of a square with a side of 8 units. This sets the ancient Egyptian value of π (pi) at
a) 3
b) 3 1/8
c) 3 1/9
d) 3 9/64
e) 3 13/81
~~~~~~~~~~~~~~~~~~~ 

This document states that

     = 8^2,

or, equivalently,

     = 64.


Thus they evaluate  as

     =  =  =  = 3 .     ANSWER

Solved.

----------------

3 is about 3.16, so it is quite good approximation to 3.14.



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