Mathematics

Problem

The difference between the areas of two concentric circular tracks is

693\pi\,\text{cm}^2

, while the difference between their circumferences is

18\pi\,\text{cm}

. a. (i) Form two equations in the radii

R

(larger) and

r

(smaller) of the tracks based on the given information. b. (ii) Solve the equations to find the exact values of

R

and

r

. c. (iii) Determine the ratio of the areas of the two tracks in its simplest form.