Billy watched a bug crawl through an arc of 24 degrees along the rim of his melon. How far did the bug crawl?

Question

Billy watched a bug crawl through an arc of 24 degrees along the rim of his melon, which was cut in half. if the radius of the melon was 5 inches, how far did the bug crawl?

Answer 1

The length of an arc, s, is given by:

 

s = r*θ

 

where:

s = arc length

r = radius

θ = angle in radians

 

The radius of the melon is r = 5 inches and the angle the bug crawled through is 24^o.  We need to convert the angle from degrees to radians.  There are pi radians in 180^o, so we can set up a proportion to determine the angle θ in radians:

 

  24^o        θ radians

------- =  ----

180^o       pi  radians

 

24*pi/180 = θ =  0.42 radians

 

s = (5 inches)*(0.42 radians) = 2.1 inches

Answer 2

total distance around assuming the melon is a sphere is the circumference = 2πr = 10π inches

 

total degrees in a circle is 360

 

the fraction of the circumference that the bug crawls is 24 degrees/360 degrees = 1/15

 

so the distance is (1/15) (10π) = 2π / 3 ≈ 2 inches