TRANSPORTATION a curve on a highway has a 1000 foot radius with lanes that are 14 feet wide. if the the curve makes a 180 degree turn, how much longer is the outside edge of the far lane than the inside edge of the close lane?​

Answer :

valenbraca

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.

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