Find the area of the biggest possible square that would fit into a circle having a radius of 3 cm

The area of the biggest possible square that fit into the circle is 18 cm²

Step-by-step explanation:

* Lets talk about the square inscribed in a circle

- The square is fit into the circle if its four vertices lie on the

  circumference of the circle

- The diagonal of the square is the diameter of the circle

- The vertices of the square divide the circle into 4 equal arcs

* Look to the attached figure

- The square ABCD fit into the circle M

- A , B , C , D lie on the circumference of the circle M

- The four arcs AB , BC , CD , AD are equal in measure and length

- The diagonal of the square is DB

- The diameter of the circle M is DB

∵ The radius of the circle is 3 cm

∵ The diameter = twice the radius

∴ The diameter of the circle = 2 × 3 = 6 cm

∴ DB = 6 cm

- The rule of the area of the square = (diagonal)²/2

∵ The length of the diagonal is 6 cm

∴ The Area of the square = (6)²/2 = 36/2 = 18 cm²

* The area of the biggest possible square that fit into the circle is 18 cm²

The area of the biggest possible square = 36 cm²

Step-by-step explanation:

From the figure attached with this answer shows that, the biggest possible square that would fit into a circle having a radius of 3 cm.

To find the area of square

Side of square  = 2 * radius of circle = 2 * 3 = 6 cm

Area of square = side * side = 6 * 6 = 36 cm²