Question

In the given figure what is the ratio of the area of the square to the circle?​

Answer 1

Answer:

Step-by-step explanation:

PQRS is a square inscribed in a circle of diameter

SQ=d which in turn has been inscribed in the square ABCD.

To find out whether ar.ABCD=4×ar.PQRS or not.

SQ=d is the diagonal of the square PQRS

Since the diameter of a circle circumscribing a square = diagonal of the same square.

∴  Any side of PQRS=PQ=  

2

d  

2

 

​  

 

​  

 

∴ar.PQRS=  

2

d  

2

 

​  

 

Again SD=d= one side of ABCD=AD.

∴ar.ABCD=AD  

2

=d  

2

 

So,  

ar.PQRS

ar.ABCD

​  

=  

2

d  

2

 

​  

 

d  

2

 

​  

=2

Ratio of area of outer square to the area of inner square is 2:1.

Answer 2

Answer:

π : 2

Step-by-step explanation:

firstly, mark all the four corners of the square as A,B,C,D

then, take a diagonal from any corner, which should divide the square into two isosceles right angle triangle.

apply Pythagoras theorem with any of the two triangle,

remember the diagonal of the square is the diameter of the circle or can be written as (2r) ; where (r) is the radius.

eg. AB²+BC²=AC²(which is 2r)

since it's an isosceles triangle AB=BC( or even if you view them as sides of a square (AB=BC=CD=DA)

just when you encounter any side ²(excluding diagonal or hypotenuse in this case) stop evaluating further and that's your area of square (s²) in relation with the radius

now use area of circle (πr²)/ area of the square obtained above, to show their ratio.

As the question suggests take the value of π = 22/7 and evaluate further

Hope that helps.!