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The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above? – OGQR 2020 Question #89 with Solution

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The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

Source OGQR 2020
Type Problem Solving
Topic Geometry
Sub-Topic Circle
Difficulty Medium – Hard

Solution

Given

In this question, we are given

  • A diagram, which is constructed by separating a circular region into 6 equal parts and rearranging them, as shown in the diagram.
  • The diameter of the circle is d.

To Find

We need to determine

  • The perimeter of the figure, as shown.

Approach & Working

The perimeter of the given figure consists of 2 parts:

  • 6 equal length arcs, which together form the perimeter of the circle
  • 2 equal line segments, each of which is equal to the radius of the circle

The total length of the 6 arcs = the perimeter of the circle = 2π * (d/ 2) = πd

The total length of the 2 line segments = (d/ 2) + (d/ 2) = d

  • Therefore, the perimeter of the given figure = πd + d

Hence, the correct answer is option D.

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