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A quadrant has a radius of 54 m. Find the perimeter of the quadrant. Take π as 3.14.

Question

A quadrant has a radius of 54 m.

Find the perimeter of the quadrant. Take π as 3.14.

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Solution

To find the perimeter of a quadrant, we need to add the length of the arc (which is a quarter of the circumference of the full circle) and twice the radius (which are the two straight lines from the center to the arc).

  1. First, let's find the circumference of the full circle. The formula for the circumference of a circle is 2πr. Here, r is the radius, which is given as 54 m. So, the circumference is 2 * 3.14 * 54 = 339.12 m.

  2. Since a quadrant is a quarter of a circle, the length of the arc of the quadrant is a quarter of the circumference. So, the length of the arc is 339.12 / 4 = 84.78 m.

  3. The perimeter of the quadrant also includes the two radii. So, we add twice the radius to the length of the arc. The radius is given as 54 m. So, the perimeter is 84.78 + 2 * 54 = 192.78 m.

So, the perimeter of the quadrant is 192.78 m.

This problem has been solved

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