Answer:
a. 400 m
b. 46.56 m
c. 461 m
Step-by-step explanation:
The perimeter is the sum of the circumference of two semicircles and the two straight sections. Two semicircles add up to one circle.
<h3>Circumference</h3>
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
<h3>Straight sections</h3>
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
<h3>a. Inner Perimeter</h3>
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.
<h3>b. Outer Radius</h3>
Above, we found the radius at the outside edge of the track to be 46.56 m.
The outer radius is 46.56 meters.
<h3>c. Outer Perimeter</h3>
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.
