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.

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(52794) (Show Source): You can put this solution on YOUR website!
.


40°  is    of the full rotation.


So,  the given area of   cm^2  is    of the total area of the circle.


It means that the total area of the circle is  .


In other words,   = .


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

     = ,  or  r =  =   cm.


ANSWER.  The radius is    cm = 1.8 cm.

Solved.

RELATED QUESTIONS
Consider the following. θ = 30°, d = 20 m (a) Find the length of the arc that... (answered by Boreal)

The radius of circle O and the measure of central angle O are given. r=6; measure of... (answered by Alan3354)

The arc length of a sector is equal to twice the radius. Express the arc length s as a... (answered by robertb)

Find the arc length of a sector that is 125� and has a radius of 20 in. Question 6... (answered by Alan3354)

the area of a sector of a circle of radius 5cm formed by an arc of length 3.5cm... (answered by Fombitz)

in a circle of radius 6 inches the length of the arc of a sector is 6 pie inches. what is (answered by robertb)

Find the arc length of a 30 degree sector of a circle with a radius of 9... (answered by josmiceli)

Find the arc length of a 30 degree sector of a circle with a radius of 9 in. (answered by fcabanski)

In a circle of radius 5 cm, a sector has a central angle 2 rad. a. Find the arc length... (answered by ikleyn)