A square measures 12 cm x 12 cm and is divided into four equal squares. If equal circles are incribed within each of the four squares, what is the circumference of each circle ?

a. 2 pi cm
b. 4 pi cm
c. 6 pi cm
d. 8 pi cm
e. 12 pi cm

please answer and explain

A square measures 12 cm x 12 cm and is divided into four equal squares. If equal circles are inscribed within each of the four squares, what is the circumference of each circle ?

So each circle has a diameter of 6 cm or a radius of 3 cm

Circumference of one circle = 2πr
= 2π(3)
= 6π

To find the circumference of each circle inscribed within the four squares, we need to determine the radius of the circle first.

Given that the square measures 12 cm x 12 cm and is divided into four equal squares, each smaller square will have sides measuring 12 cm / 2 = 6 cm.

The circle is inscribed within the smaller square, meaning it touches all four sides of the square. Therefore, the diameter of the circle is equal to the length of the side of the square.

Since the square has a side length of 6 cm, the diameter of the circle is also 6 cm.

The formula to find the circumference of a circle is C = πd, where C is the circumference and d is the diameter.

Substituting the value of the diameter into the formula, we have C = π * 6 cm.

Therefore, the circumference of each circle is 6π cm.

The correct answer is c. 6π cm.