Find the ratio of the areas of two circles whose radii are 4 cm and 7 cm.

A circles area is pi times the square of its radius or area A of the circle is given by:

A = pi*r^2

So,if the radii of the two circles are a and b, then their areas are pi*a^2 and pi*b^2, where pi is a constant = circumference/(2*radius). So, the circles'  areas  with radius a and b, are in the ratio, pi*a^2 : pi*b^2 = a^2 : b^2.

Here, a = 4cm and b=7^cm. Therefore, the circles' areas are in the ratio,  (4cm)^2  : (7cm)^2  or  in the ratio 16:49