Question

Find the radius of a circle on which a central angle measuring 2π/3 radians intercepts an arc on the circle with a length of 35π kilometers.

Answer 1

Answer:

Radius= 105/2 km

Step-by-step explanation:

The formula for arc length (in radians) is Arc Length = Radius*Angle(in radians)

The arc length is 35π km and the angle is 2π/3

Plug in the values and solve for r

35π = (2π/3)*r

35π*3/2π= r

r = 105/2 km  or 52.5 km

Answer 2

The radius of the circle is of 52.5 kilometers.

This question is solved using the length of arc formula, which states that:

$L = r\theta$

In which:

• L is the length of the arc.
• r is the radius.
• $\theta$ is the measure of the central angle, in radians.

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In this question:

• Central angle of 2π/3 radians, so $\theta = \frac{2\pi}{3}$
• Length of $35\pi$.

Thus, to find the radius, we solve for r.

$L = r\theta$

$35\pi = r\frac{2\pi}{3}$

$2\pi r = 105\pi$

Simplifying both sides by $\pi$

$r = \frac{105}{2} = 52.5$

The radius of the circle is of 52.5 kilometers.

A similar question is given at https://brainly.com/question/15162755