SOLUTION: A 6-foot-diameter disk and an 18-foot-diameter disk sit side by side. Determine the shortest length of rope that will go around both disks. my answer below is different fro

Algebra ->  Circles -> SOLUTION: A 6-foot-diameter disk and an 18-foot-diameter disk sit side by side. Determine the shortest length of rope that will go around both disks. my answer below is different fro      Log On


   

Question 31160: A 6-foot-diameter disk and an 18-foot-diameter disk sit side by side. Determine the shortest length of rope that will go around both disks.

my answer below is different from a friends with a program to figure it out. i am concerned that i am not doing it right.
For circles that are externally tangent the line of centers=the length of the sum of both radii= common external tangents
Line of centers 3+9=12
Common external tangents=12*2=24
60 degrees because we will create a equilateral triangle



Arc 1
Degrees (pi/180) r
60(3.14/180) 3
3.14
Arc 2
60(3.14/180) 9
9.42
Common external tangents+Arc 1+Arc2
24+3.14+9.42
36.56
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
GOOD TO SEE YOUR KEEN DESIRE TO DO BY YOUR SELF INSTEAD OF GOING BY A PROGRAMME
SEE THE FOLLOWING DRAWING.IT IS SELF EXPLANATORY I SUPPOSE. LET US PROCEED FROM WHERE YOU ALREADY WORKED.

LET US ESTIMATE HALF THE LENGTH NAMELY AFGE AND DOUBLE IT TO GET THE TOTAL LENGTH.
ARC AF =2*PI*3*60/360=3.14
FG=COMMON TANGENT
FG=BK=SQRT.{(9+3)^2-(9-3)^2}=SQRT.108=10.39
ARC GE=2*PI*9*120/360=18.84
TOTAL=ARC AF+FG+ARC GE = 3.14+10.39+18.84=32.37
TOTAL LENGTH=2*32.37=64.74
HOPE YOU KNOW HOW WE GOT 60 DEGREES AS SECTOR ANGLE!!!OTHERWISE I SHALL EXPLAIN YOU ON HEARING FROM YOU.