Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is 168 cm2, what is the size of the radius of the circle? (in centimeters) (a) 14 (b) 1.4 (c) 35 (d) 21

Options

A. 14
B. 1.4
C. 35
D. 21

Answer

A

Explanation

Let the radius of each circle be 'r' cm.

Then, the side of the square will be '2r' cm.
Area of the square `=(2r)^2=4r^2cm^2`
Now, according to the question.
Remaining area of the square
`=4r^2-pir^2`
`:. 4r^2-pir^2=168`
`or, r^2(4-22/7)=168`
`or, r^2xx(28-22)=168xx7`
or, `r^2=(168xx7)/6=28xx7=7xx4xx7`
`:. r=sqrt(7xx7xx4)=7xx2=14 cm`