Question

A circle has a central angle measuring startfraction 7 pi over 6 endfraction 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.

Answer 1

The radius of this circle is (B) 4.9 cm.

To find the radius of the circle:

To solve this problem, we need to, first of all, convert the angle from radians to degrees.

data;

• length of an arc = 18cm
• angle = 7/6π rads
• π= 3.14

$\frac{7\pi }{6rads} =210^{0}$

Length of an Arc:

The formula for the length of an arc is given:

$l_{arc} =$ θ/360 × $2\pi r$

Let's substitute the values and solve:

$18=\frac{210}{360} *2\pi r\\18=3.663r\\r=\frac{18}{3.663} \\r=4.9cm$

From the calculations above, the radius of this circle is 4.9cm.

Therefore, the radius of this circle is (B) 4.9 cm.

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Complete question

A circle has a central angle measuring 7pi/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