A uniform circular track is the area bounded by two concentric circles. If thearea of the track is 1144 𝑚2 and its width is 14 m, find the diameters of the twocircles.

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of the track is the difference between the areas of the two concentric circles. Let's denote the radius of the larger circle as R and the radius of the smaller circle as r.

Given that the width of the track is 14 m, we can express R as r + 14 (since the radius of the larger circle is the radius of the smaller circle plus the width of the track).

The area of the track is given as 1144 m². So, we can set up the equation:

πR² - πr² = 1144 Substituting R = r + 14 into the equation gives:

π(r + 14)² - πr² = 1144 Expanding and simplifying gives:

π(r² + 28r + 196) - πr² = 1144 π28r + π196 = 1144 28r + 196 = 1144/π 28r = 1144/π - 196 r = (1144/π - 196) / 28

Once we find the value of r, we can find R by adding 14 to r.

Finally, the diameters of the two circles are simply twice their respective radii (since the diameter is 2r). So, the diameter of the smaller circle is 2r and the diameter of the larger circle is 2R.