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Given a circle of diameter
21cm, determine the arc length subtended by a central angle of 1.2 rad. Answer to the nearest tenth.

Given a circle of diameter $21 \mathrm{~cm}$ , determine the arc length subtended by a central angle of $1$ . $2$ rad. Answer to the nearest tenth.

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Convert between customary and metric systems

Full solution

Q. Given a circle of diameter

21 \mathrm{~cm}

, determine the arc length subtended by a central angle of

1

.

2

rad. Answer to the nearest tenth.

Calculate Arc Length Formula: question_prompt: What's the arc length of a circle with a $21$ cm diameter when the central angle is $1.2$ rad?
Find Radius: The formula for arc length is $l = r \times \theta$ , where $r$ is the radius and $\theta$ is the central angle in radians.
Plug Radius and Angle: First, find the radius of the circle by dividing the diameter by $2$ . So, $r = \frac{21}{2} = 10.5$ cm.
Calculate Arc Length: Now, plug the radius and the central angle into the arc length formula. So, $l = 10.5 \times 1.2$ .
Calculate Arc Length: Now, plug the radius and the central angle into the arc length formula. So, $l = 10.5 \times 1.2$ . Calculate the arc length: $l = 10.5 \times 1.2 = 12.6$ cm.

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