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:

Let's assume the radius of first circle is $$r_1$$ and the second one is $$r_2$$.

If the area of a circle is 154 square cm.

area of a circle = $$\pi\ \times\ \left(r_1\right)^2$$

$$154=\frac{22}{7}\times\ \left(r_1\right)^2$$

$$7=\frac{1}{7}\times\ \left(r_1\right)^2$$

$$(r_1)^2 = 7^2$$

$$r_1 = 7$$ cm

The ratio of circumferences of this circle to that of the other circle, whose radius is 21 = $$2\times\ \pi\ \times\ r_1$$ : $$2\times\ \pi\ \times\ r_2$$

= $$r_1$$ : $$r_2$$

= 7 : 21

= 1 : 3