Question

Find the area of the circle in which a square of area 64 cm² is inscribed. [Use π = 3.14] 

Answer 1

We have given area of the square. 

`∴ "side"^2=64` 

`∴ "side"=8` 

Now we will find the diameter of the square.

`∴ "diagonal"=sqrt3xx"side"` 

`∴ "diagonal"=sqrt2xx8` 

`∴"diagonal"=8sqrt2`

We know that diagonal of the square is same as the diameter of the circle.

`∴ "diameter"=8sqrt2` 

`∴ "radius"=4sqrt2` 

Now we will find the area of the circle as shown below.

`∴  "area opf the circle"=pi xxr^2` 

`∴ "area of the circle"= pixx4sqrt2xx4sqrt2` 

`∴ "area of the circle"=3.14xx16xx2`

`∴ "area of the circle"=3.14xx32`

`∴ "area of the circle"=100.48`  

`"Therefore, area of the circle is" 100.48 cm^2`