SOLUTION: Assuming that the exact area of a sector determined by a 40° arc is 9/25 𝜋 cm2, find the length (in centimeters) of the radius of the circle.

Algebra ->  Formulas -> SOLUTION: Assuming that the exact area of a sector determined by a 40° arc is 9/25 𝜋 cm2, find the length (in centimeters) of the radius of the circle.      Log On


   

Question 1194226: Assuming that the exact area of a sector determined by a 40° arc is
9/25 𝜋 cm2,
find the length (in centimeters) of the radius of the circle.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

40°  is  1%2F9  of the full rotation.


So,  the given area of  %289%2F25%29%2Api cm^2  is  1%2F9  of the total area of the circle.


It means that the total area of the circle is  %2881%2F25%29%2Api.


In other words,  pi%2Ar%5E2 = %2881%2F25%29%2Api.


It implies. after reducing  common factor pi  in both sides,  that

    r%5E2 = 81%2F25,  or  r = sqrt%2881%2F25%29 = 9%2F5  cm.


ANSWER.  The radius is  9%2F5  cm = 1.8 cm.

Solved.