The arc length of a circle created by an angle of pi/3 radians is 2.5 cm. The radius of the circle is approx...
a. o.419 cm
b. 2.387 cm
c. 1.783 cm
d. 0.581 cm
Please explain how you got the answer. Thanks! :)
To find the radius of the circle, we can use the formula for arc length:
Arc Length = Radius x Angle
Given that the arc length is 2.5 cm and the angle is pi/3 radians, we can substitute these values into the formula:
2.5 cm = Radius x (pi/3)
To solve for the radius, we can rearrange the equation:
Radius = Arc Length / (pi/3)
Now we can calculate the radius:
Radius = 2.5 cm / (pi/3)
= 2.5 cm * (3/pi)
≈ 2.387 cm
Therefore, the approximate radius of the circle is 2.387 cm.
To find the radius of the circle, we can use the formula for arc length:
arc length = radius x angle
Given that the arc length is 2.5 cm and the angle is π/3 radians, we can substitute these values into the formula:
2.5 cm = radius x π/3 radians
To isolate the radius, we need to divide both sides of the equation by π/3 radians:
2.5 cm ÷ (π/3 radians) = radius
To simplify this expression, we can multiply the numerator and denominator by the reciprocal of π/3, which is 3/π:
2.5 cm ÷ (π/3 radians) x (3/π) = radius
Simplifying further, we get:
2.5 cm x 3/π x 3/π = radius
Now we can calculate the approximate value of the radius using a calculator:
radius ≈ 2.387 cm
Therefore, the correct answer is b. 2.387 cm.
Kathy/Julie -- please use the same screen name for your posts.
arc = rØ , where r is the radius and Ø is the central angle.
2.5 = r(π/3)
r = 7.5/π or appr. 2.387