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प्रश्न
The area of a circle is 220 cm2. The area of ta square inscribed in it is
विकल्प
49 cm2
70 cm2
140 cm2
150 cm2
उत्तर
∴
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`
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