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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? – OGQR 2020 Question #99 with Solution

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?

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicCircle / Square
DifficultyMedium – 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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