Answer :
Answer:
The outside edge is 44 ft longer than the inside edge.
Step-by-step explanation:
The outside edge has a 1000 ft radius. Because the curve makes a 180° turn, the length of the curve is half of the perimeter of a circle.
Perimeter of a circle:
[tex]P=\pi \times 2R[/tex]
Outside length of the curve is given by:
[tex]O=\frac{P}{2} =\frac{\pi \times 2R}{2} = \pi \times R[/tex]
R=1000 ft
Then,
[tex]O= \pi \times R= \pi \times 1000 ft= 3141.6 ft [/tex]
Inside length of the curve is given by:
r=R-14 ft
[tex]O= \pi \times r=\pi \times( R-14 ft )= \pi \times (1000 ft - 14 ft)= \pi \times 986 ft= 3097.6 ft [/tex]
The difference between the two lengths is:
[tex]\Delta L=O-I=3141.6 ft-3097.6 ft= 44 ft[/tex]
The outside edge is 44 ft longer than the inside edge.