In terms of diameter (d), the area (A) of a circle is given by
A = (π/4)d²
For your larger circle ...
A = (π/4)*(24 km)²
A = 144π km² . . . . . . . . area of larger circle
For your smaller circle ...
A = (π/4)*(8 km)²
A = 16π km² . . . . . . . . . area of smaller circle
The ratio of the two areas is
(larger area)/(smaller area) = ((π/4)*(24 km)²) / ((π/4)*(8 km)²)
= (24/8)² . . . . . . . . . . . . π/4, km cancel, so it simplifies to this
= 3²
= 9 . . . . . . this many small circles have the same area as the larger circle
Changing km to ft does not change the ratio of areas.
