36. A chord subtends an angle of $$ 120^{\circ} $$ at the centre of a circle of radius 3.5 cm . Find the perimeter of the minor sector containing the chord $$ \left[\right. $$ Take $$ \left.\pi=\frac{22}{7}\right] $$ A. $$ 14 \frac{1}{3} \mathrm{~cm} $$ B. $$ 12 \frac{5}{6} \mathrm{~cm} $$ C. $$ B \frac{1}{7} \mathrm{~cm} $$ D. $$ 7 \frac{1}{3} \mathrm{~cm} $$ 7. If $$ \sin x=\frac{5}{4} $$ and

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We are given a circle with radius $$ r = 3.5 $$ cm and a chord that subtends an angle of $$ 120^\circ $$ at the centre. The perimeter of the minor sector is the sum of the arc length and the lengths of the two radii.

1. **Convert the angle into radians**

The angle in radians is:
   $$
   \theta = 120^\circ \times \frac{\pi}{180^\circ} = \frac{2\pi}{3}.
   $$

2. **Calculate the arc length**

The arc length $$ L $$ is given by:
   $$
   L = r \theta = 3.5 \times \frac{2\pi}{3} = \frac{7\pi}{3}.
   $$
   
   Given $$ \pi = \frac{22}{7} $$, substitute this value:
   $$
   L = \frac{7}{3} \times \frac{22}{7} = \frac{22}{3} \text{ cm}.
   $$

3. **Find the total perimeter of the sector**

The perimeter $$ P $$ of the minor sector is the sum of the arc length and the two radii:
   $$
   P = L + 2r = \frac{22}{3} + 2 \times 3.5.
   $$
   
   Calculate the sum:
   $$
   2 \times 3.5 = 7 \text{ cm},
   $$
   $$
   P = \frac{22}{3} + 7 = \frac{22}{3} + \frac{21}{3} = \frac{43}{3} \text{ cm}.
   $$

4. **Express the perimeter as a mixed number**

Converting $$\frac{43}{3}$$ to a mixed number:
   $$
   \frac{43}{3} = 14 \frac{1}{3} \text{ cm}.
   $$

Thus, the perimeter of the minor sector is $$ 14 \frac{1}{3} $$ cm.
The perimeter of the minor sector is $$ 14 \frac{1}{3} $$ cm.

A chord subtends an angle of at the centre of a circle of radius 3.5 cm . Find
the perimeter of the minor sector containing the chord Take
A. B. C.
D.

If and

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