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Question
A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square.
Solution
Let the side of a square be a and the radius of circle be r.
Given that, length of diagonal of square = 8 cm
⇒ `asqrt2 = 8`
⇒ `a = 4sqrt2` cm
Now, Diagonal of a square = Diameter of a circle
⇒ Diameter of circle = 8
⇒ Radius of circle = r = `"Diameter"/2`
⇒ `r = 8/2 = 4` cm
∴ Area of circle = `pir^2 = pi(4)^2`
= `16pi xx cm^2`
and Area of square = `a^2 = (4sqrt2)^2`
= 32 cm2
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