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