A quadrant has a radius of 67 m. Find the perimeter of the quadrant. (Take π as 3.14)
Question
A quadrant has a radius of 67 m. Find the perimeter of the quadrant. (Take π as 3.14)
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 represents the two straight sides of the quadrant).
Step 1: Find the circumference of the full circle. The formula for the circumference of a circle is 2πr. Here, r is the radius, which is 67 m. So, the circumference is 2 * 3.14 * 67 = 421.64 m.
Step 2: Find the length of the arc of the quadrant. Since a quadrant is a quarter of a circle, the length of the arc is a quarter of the circumference. So, the length of the arc is 421.64 / 4 = 105.41 m.
Step 3: Add the length of the arc to twice the radius to find the perimeter of the quadrant. The radius is 67 m, so twice the radius is 2 * 67 = 134 m. Adding this to the length of the arc gives 105.41 + 134 = 239.41 m.
So, the perimeter of the quadrant is 239.41 m.
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