Question

A sector of a circle with radius 14 cm makes an angle 90° at the centre. Then the perimeter of the sector is (in cm).

• A. 14 + 7π
• B. 7 + 14π
• C. 7 + 28π
• D. 28 + 7π

Hint:

Remember to convert the angle to radians before using the formula for the perimeter of a sector.

Answer 1

The Correct Option is A

Step 1: Understanding the formula.
The perimeter \( P \) of a sector is given by:
\[ P = 2r + \theta \cdot r \] where \( r \) is the radius and \( \theta \) is the angle in radians.

Step 2: Convert the angle to radians.
For an angle of \( 90° \), the angle in radians is:
\[ \theta = \frac{90°}{180°} \cdot \pi = \frac{\pi}{2} \]

Step 3: Calculate the perimeter.
Substitute the values \( r = 14 \) cm and \( \theta = \frac{\pi}{2} \) into the perimeter formula:
\[ P = 2(14) + \frac{\pi}{2} \cdot 14 = 28 + 7\pi \]

Step 4: Conclusion.
Therefore, the perimeter of the sector is \( 28 + 7\pi \) cm.

Final Answer: 28 + 7π.