If the area of a circle is 154 square cm, then the ratio of circumferences of this circle to that of the other circle, whose radius is 21 cm, is:

1 : 3

We know that,

Area of circle = πr²

Area of circle1 = 154 cm²

Radius of circle2 = 21 cm

= 154 = \(\frac{22}{7}\)× radius²

= radius² = 49

= Radius = \(\sqrt {49}\) = 7cm

So the circumference of cicle₁ = 2πr = 2 × \(\frac{22}{7}\)× 7 = 44 cm

Radius of circle₂ = 21 cm

Circumference of circle₂  = 2 × \(\frac{22}{7}\)× 21 = 132

Ratio of Circumference of circle₁ : Circumference of circle₂ = 44 : 132 = 1 : 3