# How To Find The Perimeter Of A Sector

The formula for the circumference of a circle is 2πr. But the formula for the circumference of an arc is far from simple. The area is a part of a circle or you can call it a slice like you see in a pizza. The circumference of an arc in a circle depends on the angle it makes at the center. The perimeter of an area is called the perimeter of the area. In this article, we discuss the formula for calculating the perimeter of an arc in a circle.

**Formula to calculate the perimeter of an area**

Contents

Derive the formula for the circumference of a circle with radius r. Read: how to find the perimeter of an arcFormula for perimeter of an arc In the figure above, you can see a circle with radius r and arc angle θ. We can clearly see that the circumference will be the sum of radius + radius + arc length = 2r + arc length. θ arc length suppose to be => using unary method x = (θ / 360) * 2πr ———- (1) So the formula for arc circumference would be:** 2r + (θ / 360) * 2πr = 2r[1 + (θ*π)/180]**

**What is the largest possible circumference of a circle?**

The formula for the perimeter of an area is 2r[1 + (θ*π)/180]. The maximum possible value θ that can be achieved is 360o. But at θ = 360, there will be no sector, it will be a complete circle. So, θ can be obtained for any value less than 360. At 360, the value of the area perimeter becomes 2r + 2πr. So the value of arc circumference is always <(2r + 2πr).

**What is the smallest possible perimeter of an area?**

The smallest possible value of θ is 0o. But at θ = 0, there will be no sector, it will be a complete circle. So, θ can be obtained for any value greater than 0. At 0, the value of the area perimeter will be 2r. So the value of arc circumference is always > 2r Read more: How to melt chocolate kisses in the microwave | Top Q&A Area perimeter value range:** 2r (2r + 2πr).**

**Unit for the circumference of an arc in a circle**

The units for perimeter will always be in units like cm, meters, feet, km, etc. But the unit of area of an area will be square units like m2, cm2, km2, etc.

**Calculator for area perimeter**

You can use this calculator to calculate the circumference of an arc. You can use this calculator to calculate the circumference of an arc based on the angle and radius of the arc. You can also calculate arc length and arc area using this tool.

**Number:**

**A circle with a radius of 10 m has a part formed at an angle of 60° with the center. Find the perimeter of the area. (π = 3.14)**Given values => radius = 10 m; angle of arc at center = 60° Formula for perimeter of arc = 2r[1 + (θ*π)/180]So perimeter = 20[1+ (60*3.14)/180] = 40.92 m**The arc length of an arc in a circle is 40 cm. The area of the complete circle is 628 cm2. Find the perimeter of the area.**Sector area = πr2 = 628Read more: how to unmerge layers in photoshop | Peak Q & Ar = 4.47 cm**The area of the circle is 628 cm2. An arc in a circle forms an angle of 60°** **st at the center of the circle. Find the arc length of the arc**.Area of circle = πr2 = 628 means r = 4.47 cm Shape for perimeter of an area = 2r[1 + (θ*π)/180]circumference = 2 * 4.47[1+ (60*3.14)/180] = 18.2972 Measure = 2 * radius + arc length18.2972 = 2 * 4.47 + arc length = 18.2972 – 8.94 = 9.35 cm

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