A circular park of 28 m diameter has been constructed. A 3.5m circular track outside has been developed along the park. Using algebric formulae, find the area of the track around the park.
subtract area of inside circle from area of outside circle
radius inside = 28/2 = 14
radius outside = 14+3.5 = 17.5
so
pi(17.5^2-14^2)
Subtract area of inside circle from area of outside circle
To find the area of the circular track around the park, we need to subtract the area of the park from the area of the larger circle formed by the track.
The area of a circle is given by the formula: A = πr², where A is the area and r is the radius. However, in this case, we are given the diameter of the park and track, so we need to convert it to radius first.
The radius of the park is half the diameter, so r = 28m/2 = 14m.
The radius of the track will be the sum of the radius of the park and the width of the track, so r_track = 14m + 3.5m = 17.5m.
Now we can find the area of the circle with the track using the formula: A_track = πr_track².
Substituting the value of r_track, we have:
A_track = π(17.5m)²
A_track = π(306.25m²)
A_track ≈ 961.94m²
So, the area of the track around the park is approximately 961.94 square meters.