Question

The area of a circle is 220 cm². The area of ta square inscribed in it is

Options

• 49 cm²

• 70 cm²

•  140 cm²

•  150 cm² 

Answer 1

∴

Let BD be the diameter and diagonal of the circle and the square respectively.

We know that area of the circle `=pir^2`

Area of the circle  =`pir^2`

`∴ 220=22/7xxr^2`

Multiplying both sides of the equation by 7 we get, 

`220xx7=22xxr^2`

Dividing both sides of the equation by 22 we get,

`∴ r^2=70`

`∴r=sqrt70`

As we know that diagonal of the square is the diameter of the square.

`∴ "Diagonal"=2r`

`∴ "Diagonal"=2sqrt70`

`∴ "side of the square"= "diagonal"/sqrt2`   ................(1)

Substituting Diagonal=`2sqrt70` in equation (1) we get,

side of the square=`(2sqrt70)/2`

∴ side of the square= `2sqrt(70/2)`

∴ side of the square=`2sqrt35`

∴ Area of the square=`"side "^2`

                                 =`(2sqrt35)^2`

                                 =`4xx35`

                                 = `140`

Therefore, area of the square is.`140 cm^2`