Question

find the area of circles in which a square of area 64cm2 is inscribed

Answer 1

side of square=8cm
perimeter=32cm
perimeter of square =circumference of circle
32=2×22÷7×R
Radius=find

area of circle =find

Answer 2

Answer:

The area of the circle is $A=100.48 cm^2$

Step-by-step explanation:

Given : A square of area 64 sq.cm.

To find : The area of the circle in which square is inscribed?

Solution :

Area of the square  is $A=64 cm^2$

So the side of this square  is $s=\sqrt{64}=8 cm$

And the diagonal of this square is $d=s\sqrt{2}=8\sqrt{2}$

Given that the square is inscribed inside the circle,

The diagonal of this square  is equal to  the diameter  of the circle.

$D=8\sqrt{2}$

Radius is $R=\frac{D}{2}$

$R=\frac{8\sqrt{2}}{2}$

$R=4\sqrt{2}$

Area of the circle is

$A=\pi R^2$

$A=\pi (4\sqrt{2})^2$

$A=3.14\times 16\times 2$

$A=100.48 cm^2$

Therefore, The area of the circle is $A=100.48 cm^2$