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If a square is inscribed in a circle, fi...

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Text Solution

Verified by Experts

The correct Answer is:
`pi:2`
Let the radius of the circle be `r cm`
Then diagonal of the square `=` diameter of the circle `=2rcm`
Area of the circle `=(pir^(2))cm^(2)`
Area of the square `=1/2xx("diagonal")^(2)=1/2xx4r^(2)=(2r^(2))cm^(2)`

`:.` Required ratio `=pir^(2):2r^(2)=pi:2`
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