OGQR 2020: Question No. 99
The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Circle / Square |
| Difficulty | Medium – Hard |
Solution
Given
In this question, we are given
- The figure of a drop-leaf table.
- With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle.
To Find
We need to determine
- The radius, in meters, of the tabletop when all four leaves are up.
Approach & Working
When all four leaves are up, the table will look like the following:
In this case, the diameter of the circle is equal to the diagonal of the table.
- As the square table has a side length of 1m, its diagonal will be √2 m.
- Hence, diameter of the circular table = √2 m.
- Therefore, radius of the table = √2 / 2 m
Hence, the correct answer is option B.
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