Question

6) A circle and a square have the same area. The ratio of the side of the square and the radius of the circle is
:
A. √ π:1
B.

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

If the circle’s radius is  r , and the side of the square is  a , then for the area of the circle and the square we have, respectively:

S1=πr2  

S2=a2  

But, according to the problem statement

S1=S2=>πr2=a2=>a2r2=π=>(ar)2=π  

Therefore, the ratio of the side of the square and the radius of the circle is

ratio=(ar)=π−−√  

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James Buddenhagen, lives in Xico,Veracruz.Mexico (2006-present)

Answered February 9, 2020 · Author has 2.5K answers and 1.3M answer views

Originally Answered: A circle and a square both have an area of A. What is the exact ratio of the side length of the square to the radius of the circle?

A circle and a square both have an area of A. What is the exact ratio of the side length of the square to the radius of the circle?

To make it easy say  A=1 .

Then side of square is 1, and for circle must solve

πr2=1  for  r , the radius, getting:

r=1π√  

So the answer is:  1:1π√ , or multiplying both parts by  π−−√ , the same ratio is  π−−√:1 .

(this is approximately 1.77 : 1)

Now you must still show that choosing  A=1  had no effect on the answer.