Question

there is a square of side 6 cm. a circle is inscribed inside the square. find the ratio of the area of circle to square.

Answer 1

side of square=6cm
area of square=side×side
=6×6
=36sq.cm
a circle is inscribed inside the square
so, side of square=diameter of the circle
d=6cm
r=d/2=6/2=3cm
area of circle=πr^2
=π×3×3
=9π

the ratio of the area of circle to square.
=9π:36
=π:4

Answer 2

Answer: The ratio of the area of circle to square is π:4.

Step-by-step explanation:

Given that:

• Side of square= 6cm.
• A circle is inscribed inside the square.

We have to find the ratio of the area of circle to square.

Finding the area of square:

We know that, area of square;

• $A_{S}=(Side)^{2}$

Side given as 6cm, putting the value;

$A_{S}=(6)^{2}=36sq.cm$      (Equation 1)

Finding the area of circle inscribed:

We know that, area of circle;

• $A_{C}=\pi R^{2}$

As the circle is inscribed in the square,

So, side of the square = diameter of the circle

S=D=6

and we know; $R=\frac{D}{2}$

Putting the values, we get;

$R=\frac{D}{2}=\frac{6}{2}=3$

Therefore, the area of circle is:

$A_{C}=\pi R^{2}=\pi 3^{2} =9\pi$     (Equation 2)

Finding the ratio:

Area of circle: Area of square=$9\pi :36$

$A_{C}: A_{S} = \pi : 4$

Hence, the ratio of area of circle to square is $\pi : 4$.