Question : Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. If each side of the squares is 140 cm, then the area of the space enclosed between the circumference of the circle is: (Take $\pi=\frac{22}{7}$)
Option 1: 4200 cm2
Option 2: 2100 cm2
Option 3: 7000 cm2
Option 4: 2800 cm2
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Correct Answer: 4200 cm 2
Solution :
Given: Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. Each side of the squares is 140 cm.
Each side of the square ($a$) = 140 cm
The radius of the circles ($r$) = 70 cm
The area of the enclosed space = (Area of the square) – (Area of 4 quadrants i.e. the area of a circle)
So, the area of the enclosed space
= $a^2 - \pi r^2$
= $140^2-(\frac{22}{7}×70×70)$
= $19600 – 15400$
= 4200 cm
2
Hence, the correct answer is 4200 cm
2
.
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