Answer:
a. 400 m
b. 46.56 m
c. 461 m
Explanation:
The perimeter is the sum of the circumference of two semicircles and the two straight sections. Two semicircles add up to one circle.
Circumference
The circumference of a circle is given by the formula ...
C = 2πr
For an inner radius of 36.8 m, the circumference of the inner circle is ...
C = 2π(36.8 m) = 73.6π m
The outer perimeter will have a radius that is the sum of the inner radius and the width of 8 track lanes.
r = 36.8 m + 8(1.22 m) = 46.56 m . . . . . . . . . outer semicircle radius
The circumference of the outer circle is ...
C = 2π(46.56 m) = 93.12π m
Straight sections
The straight sections are the same length on both perimeters. The sum of the two straight section lengths is ...
2 × 84.39 m = 168.78 m
a. Inner Perimeter
The inner perimeter is the sum of the inner circumference and the length of the straight sections:
P = 73.6π m + 168.78 m ≈ 231.2 m + 168.8 m = 400 m
The inner perimeter is about 400 meters.
b. Outer Radius
Above, we found the radius at the outside edge of the track to be 46.56 m.
The outer radius is 46.56 meters.
c. Outer Perimeter
The outer perimeter is the sum of the outer circumference and the length of the straight sections:
P = 93.12π m +168.78 m ≈ 292.5 m + 168.8 m ≈ 461 m
The outer perimeter is about 461 meters.