What is the perimeter of a quadrant of a circle of radius r?

A quadrant of a circle is one-fourth (¼) of the full circle. It consists of:

• A curved arc (¼ of the circumference of the circle)
• Two straight radii connecting the arc ends to the center

To find the perimeter of a quadrant, you need to add the length of:

1. The arc (which is ¼ of the circumference)
2. Two radii

Formula for Perimeter of a Quadrant

Perimeter of a quadrant=41​×2πr+2r=2πr​+2r

Where:

• rrr = Radius of the circle
• π≈3.1416\pi \approx 3.1416π≈3.1416

Comparison Table: Circle vs Quadrant

Feature	Full Circle	Quadrant
Area	πr2\pi r^2	14πr2\frac{1}{4} \pi r^2
Circumference	2πr2\pi r	14×2πr=πr2\frac{1}{4} \times 2\pi r = \frac{\pi r}{2}
Perimeter (including radii)	Not applicable	πr2+2r\frac{\pi r}{2} + 2r
Number of radii (used)	Not part of perimeter	2 radii

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