The length of the arc of a sector is calculated using the formula L = (θ)/(360^°) × 2π r. Substituting the given values for θ and r, and using π = (22)/(7), we find the arc length.

If the sector of a circle with diameter 14 cm makes an angle $90^\circ$ at the centre, then the perimeter of the sector is :

Answer: The perimeter of the sector is $25\text{ cm}$ .

Step-by-step solution

Step 1: Identify given values

The problem provides the diameter of the circle as 14 cm and the angle subtended by the sector at the center as $90^\circ$ . We first calculate the radius from the given diameter.

Step 2: Calculate the length of the arc

The length of the arc of a sector is calculated using the formula $L = \frac{\theta}{360^\circ} \times 2\pi r$ . Substituting the given values for $\theta$ and $r$ , and using $\pi = \frac{22}{7}$ , we find the arc length.

Step 3: Calculate the perimeter of the sector

The perimeter of a sector is the sum of the arc length and twice the radius (since the two radii form the straight sides of the sector). We add the calculated arc length to twice the radius to find the total perimeter.

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If the sector of a circle with diameter 14 cm makes an angle 90∘90^\circ90∘ at the centre, then the perimeter of the sector is :