A circle has a central angle measuring \(\frac{7\pi}{6}\) radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for Pi. (A) 3.7 cm (B) 4.9 cm (C) 14.3 cm (D) 15.4 cm
Answer (1)
To find the length of the radius of the circle, we can use the formula for the arc length, which is given by:
L = r θ
where L is the arc length, r is the radius of the circle, and θ is the central angle in radians.
In this problem, we know:
L = 18 cm (the arc length)
θ = 6 7 π radians (the central angle)
We need to find r , the radius of the circle.
Plugging the known values into the formula, we get:
18 = r × 6 7 π
To solve for r , we rearrange the equation:
r = 7 π 18 × 6
Now, substituting π = 3.14 :
r = 7 × 3.14 18 × 6 ≈ 21.98 108
Calculating the value:
r ≈ 21.98 108 ≈ 4.9
Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 4.9 cm.
The correct answer is option (B) 4.9 cm.
