Find the area of the circle in which a square of area $ 64 \mathrm{~cm}^{2} $ is inscribed. [Use $ \pi=3.14 $ ]

Academic Mathematics NCERT Class 10

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 $100.48\ cm^2$.

Simply Easy Learning

Updated on: 10-Oct-2022

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