SOLUTION: A square is inscribed in a circle. If the area of the square is 9 in squared, what is the ratio of the circumference of the circle to the area of the circle?
Question 1065051: A square is inscribed in a circle. If the area of the square is 9 in squared, what is the ratio of the circumference of the circle to the area of the circle?
Found 2 solutions by ikleyn, KMST:Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website! .
A square is inscribed in a circle. If the area of the square is 9 in squared, what is the ratio of the circumference of
the circle to the area of the circle?
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The ratio of the the circumference of the circle to the area of the circle is
= .
We are given = 9.
Hence, a = 3.
Therefore, r = = .
Then the ratio of the circumference of the circle to the area of the circle is = = .
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website! NOTE: This is a strange problem wording,
and I suspected a typo in the wording you posted.
If so, check the wording carefully and post again.
For a square , <---> .
In this case, for the square in the problem, .
With the square inscribed in a circle ,
the diameter, , of the circle
is the diagonal, , of the square.
According to the Pythagorean theorem, ,
so .
For any circle, , , and
circumference=pi*diameter=pi*radius/2}}} .
For any circle,
the ratio of circumference of the circle to the area of the circle is .
For the circle in the problem, ,
and we could calculate that ratio as ,
with units of or .
Maybe you were expected to calculate , , ,
and then further calculate the ratio as ,
with units of or .