If O is the Center Of The Circle, What is The Perimeter Of The Sector GMAT Problem Solving

Question:

If O is the center of the circle, what is the perimeter of the sector with central angle 72°?

1. 5 + 2π
2. 10 + 2π
3. 10 + 4π
4. 10 + 5π
5. 20 + 2π

‘If O is the center of the circle, what is the perimeter of the sector with central angle 72°?’ –  is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical understanding. 

Solution and Explanation:

Approach Solution 1:

There is only one way to solve this problem.

Labelling the two points as A and B, where the centre is O. The points as A and B where radius touch the circumference of the circle O.
Perimeter of minor Sector AOB = radius + radius + minor Arc length AB
We know radius (r) = 5
minor Arc length AB =\(\frac{72}{360}\)x2πr=\(\frac{1}{5}\)x10π=2π
Therefore, perimeter of minore sector AOB=5+5+2π=10+2π
Hence the required answer is option B.

Correct Answer: B

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