OGQR 2020: Question No. 94
In the racetrack shown above, regions I and III are semi-circular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Circle / Rectangle |
| Difficulty | Medium |
Solution
Given
In this question, we are given
- The diagram of a racetrack consists of two semi-circular regions, with radius r, and one rectangular region.
- The length of the rectangular region is twice its width.
To Find
We need to determine
- The perimeter of the track, expressed in terms of r.
Approach & Working
The perimeter of each semi-circular region = πr
- Therefore, the perimeter of both semi-circular regions together = 2πr
The rectangular region has length twice its width.
- Width of the rectangular region = diameter of the semi-circular region = 2r
- Hence, length of the rectangular region = 2 * 2r = 4r
Therefore, the perimeter of the whole region = 2πr + 4r + 4r = 2πr + 8r = 2r (π + 4)
Hence, the correct answer is option B.
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