Question

The radius of the circle whose arc of length 15 cm makes an angle of 3/4 radian at the centre, is

• A. 10 cm
• B. 20 cm
• C. \(11\frac{1}{4}\) cm
• D. \(22\frac{1}{2}\) cm

Hint:

\(\theta\) must be in radians for \(s = r\theta\).

Answer 1

The Correct Option is B

To find the radius of a circle given the length of an arc and the angle it subtends at the center, we can use the formula for the arc length of a circle:

\(L = r \theta\)

Where:

• \(L\) is the length of the arc,
• \(r\) is the radius of the circle, and
• \(\theta\) is the central angle in radians.

Given:

• Arc length, \(L = 15\) cm
• Central angle, \(\theta = \frac{3}{4}\) radians

We need to find the radius \(r\). Substitute the known values into the formula and solve for \(r\):

Rearrange the formula to solve for \(r\):

\(r = \frac{L}{\theta}\)

Substitute the given values:

\(r = \frac{15}{\frac{3}{4}}\)

To solve \(\frac{15}{\frac{3}{4}}\), multiply by the reciprocal of \(\frac{3}{4}\):

\(r = 15 \times \frac{4}{3}\)

\(r = \frac{60}{3}\)

\(r = 20\)

Thus, the radius of the circle is 20 cm.

The correct answer is 20 cm.