Question

four Street feed into a roundabout Circle as shown below. if the diameter of the roundabout is 30 feet, find the approximate distance a car will travel between Cole Street and Male Street along the roundabout. Round to the nearest tenth of a foot.

Answer 1

the central angle of the arc is 105 degrees

step 1

Find the length of the complete circle

C=2pi(r)

we have

pi=3.14

r=30/2=15 ft

substitute

C=2(3.14)(15)

C=94.2 ft

Remember that the complete circle subtend a central angle of 360 degrees

so

Applying proportion

Find out the length of the arc by a central angle of 105 degrees

so

94.2/360=x/105

solve for x

x=105*94.2/360

x=27.5 ft

answer is 27.5 ft