SOLUTION: hello could you please help me with this problem-thank you The circumference of a circle (measured in inches) is 2/3 the area of the circle (measured in square inches). What is

Algebra ->  Circles -> SOLUTION: hello could you please help me with this problem-thank you The circumference of a circle (measured in inches) is 2/3 the area of the circle (measured in square inches). What is      Log On


   

Question 1152782: hello could you please help me with this problem-thank you
The circumference of a circle (measured in inches) is 2/3 the area of the circle (measured in square inches). What is the circle's radius?
Found 2 solutions by math_helper, MathLover1:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



+2%2Api%2AR+=+%282%2F3%29pi%2AR%5E2+



Cancel factors appearing on both sides:

+cross%282%2Api%2AR%29+=+%28cross%282%29%2F3%29cross%28pi%2AR%29%2AR+

Multiply both sides by 3:

++3+=+R+



+highlight%28+R+=+3+in%29+

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The circumference of a circle is:
C=2r%2Api
the area of the circle is:
A=r%5E2%2Api
if the circumference of a circle is 2%2F3 the area of the circle, we have
C=%282%2F3%29A.......substitute C and A
2r%2Api=%282%2F3%29r%5E2%2Api...simplify
2cross%28r%29%2Across%28pi%29=%282%2F3%29r%5Ecross%282%29%2Across%28pi%29
2=%282%2F3%29r
r=2%2F%282%2F3%29
r=6%2F2
r=3
check:
C=2r%2Api=>C=2%2A3%2Api=>C=6%2Api
A=r%5E2%2Api=>A=3%5E2%2Api=>A=9%2Api
C=%282%2F3%29A=>C=%282%2F3%299pi=%2818%2F3%29pi=6pi