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Find the area of the circle in which a square of area $ 64 \mathrm{~cm}^{2} $ is inscribed. [Use $ \pi=3.14 $ ]
Given:
A square of area \( 64 \mathrm{~cm}^{2} \) is inscribed in a circle.
To do:
We have to find the area of the circle.
Solution:
Let the side of the square be $a$.
Area of the square $= 64\ cm^2$
This implies,
Side of the square $a=\sqrt { 64 } = 8\ cm$
The square in inscribed in the circle.
This implies,
Diagonal of the square $=$ Diameter of the circle.
Radius of the circle $=\frac{1}{2} \times$ Diagonal of the square
$r=\frac{1}{2} \times \sqrt{2}a$
$ = \frac{1}{2} \times \sqrt{2}(8)\ cm$
$= 4\sqrt{2}\ cm$
Therefore,
Area of the circle $= \pi r^2$
$= 3.14 \times (4\sqrt{2})^2\ cm^2$
$= 3.14 \times 32$
$= 100.48\ cm^2$
The area of the circle is $100.48\ cm^2$.
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