Inscribed Square

[smclean23]

Let S be the length of the side of a square inscribed in a circle of radius R. Which of the following represents the ratio of the area of the circle to that of the square?

Pi/2
2r
Pi(r)
4Pi(r^2)
8Pi(r^2)

What is the methodology?



A

[eccentric]

The square inscribed in a circle has diagonal as diameter of circle.
The half of square makes a 45-45-90 triangle
with hyp as 2R
thus (2R)^2 = x^2+x^2 = 2x^2 area of square is 2R^2
and area of circle is pi R^2
thus ratio of area of circle to area of square is pi/2

[Gaurav Tyagi]

A first look at this problem gives me an idea that any answer to this problem cannot contain any variable R or S as it is asking for a ratio of squares in which either both R and S should be there in the answer or none of them. Hence, I can eliminate b,c,d and e.

[smclean23]

I got everything you said except how u got the hyp as 2R and the area of the circle being 2R^2.....thanks in advance for the help

[sibbineni]

how u got the hyp as 2R

since in question it is given the radius=R

here diameter=2*R

so hypotenuse-->2R

u mean area of square....

side^2