Question

Four equal circles are described about the four corners of a square so that each circle touches two of the others. Find the area of the space enclosed between the circumstances of the circles, each side of the square measuring 24 cm.

Answer 1

r=24 cm
area enclosed between one circle circumference and square boundary = 1/4 × area of circle
now there are 4 circles .. hence total area enclosed = 4× above calculated area

thus answer is 576π cm square

Answer 2

Diameter=24

Radius=d÷2=12

Area of square=S×S=24×24=576cm2

Area of circle=πr2=22÷7×12×12=22÷7×144=

452.5cm2

Now the area of the space enclosed=

576-452.5=123.5cm2....