Question

If the ratio of the area of two circles is 1:4, then the ratio of their circumference .......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 1:4
(b) 1:2
(c) 4:1
(d) 2:1

Answer 1

Let the radii of circles be a and b

A1 / A2 = 1 /4

=> pi a^2 / pi b^2 = 1/ 4

=> a^2 / b^2 = 1/ 4

=> a / b = 1/2 -----(1)

Now,

C1 / C2 = 2 pi a / 2 pi b

= a/ b

= 1/2

= 1 : 2

Answer 2

Option ( b ) is correct.

Explanation :

Let r , R are radii of two circles.

Ratio of areas = 1 : 4

=> ( πr²/πR² ) = ( 1/2 )²

=> ( r/R )² = ( 1/2 )²

=> r/R = 1/2 ----( 1 )

Ratio of their Circumference

= ( 2πr )/( 2πR )

= r/R

= 1/2 [ from ( 1 ) ]

= 1 : 2

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