An arc AB of a sector of a circle subtends an angle 110° at the centre of the circle. Find the angle subtended by the arc at the circumference.

March 21, 2026Mathematics

ScanSolve AI Answer

March 21, 2026

Answer

9 \ cm

Step 1: The formula for the length of an arc is
$l = r \theta$
where $l$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians.

Step 2: Convert the central angle from degrees to radians:
$\theta = 60^\circ \times \frac{\pi}{180} = \frac{\pi}{3}$ radians.

Step 3: Substitute the known values into the formula ( $l = 3\pi$ cm, $\theta = \frac{\pi}{3}$ rad):
$3\pi = r \times \frac{\pi}{3}.$

Step 4: Solve for the radius $r$ :
$r = 3\pi \div \frac{\pi}{3} = 3\pi \times \frac{3}{\pi} = 9.$
The radius of circle B is $9$ cm.

$\boxed{9 \ cm}$

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Quick Answer

The formula for the length of an arc is l = r where l is the arc length, r is the radius, and is the central angle in radians.

Asked on March 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 21, 2026

Step 1: The formula for the length of an arc is l = r where l is the arc length, r is the radius, and is the central angle in radians. Step 2: Convert the central angle from degrees to radians: = 60^ × ()/(180) = ()/(3) radians. Step 3: Substitute the known values into the formula (l = 3 cm, = ()/(3) rad): 3 = r × ()/(3). Step 4: Solve for the radius r: r = 3 ÷ ()/(3) = 3 × (3)/() = 9. The radius of circle B is 9 cm. 9 \ cm