Question

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 1

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:

$P=\pi \times 2R$

Outside length of the curve is given by:

$O=\frac{P}{2} =\frac{\pi \times 2R}{2} = \pi \times R$

R=1000 ft

Then,

$O= \pi \times R= \pi \times 1000 ft= 3141.6 ft$

Inside length of the curve is given by:

r=R-14 ft

$O= \pi \times r=\pi \times( R-14 ft )= \pi \times (1000 ft - 14 ft)= \pi \times 986 ft= 3097.6 ft$

The difference between the two lengths is:

$\Delta L=O-I=3141.6 ft-3097.6 ft= 44 ft$

The outside edge is 44 ft longer than the inside edge.