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# Perimeter of a Sector Calculator

## Perimeter of a Sector Calculator

A Perimeter of a Sector Calculator is a tool used to calculate the perimeter or the curved boundary of a sector of a circle. A sector is a portion of a circle defined by two radii and the arc between them.

Perimeter of a Sector Calculator:

To calculate the perimeter of a sector, you need to know the radius of the sector (r) and the angle of the sector (θ) in radians. The perimeter of a sector is the total length of its boundary, which includes the arc and the two radii. Like Perimeter of a sector, you may also use Economic Value Added Calculator.

## Formula for Perimeter of a Sector Calculator

The formula for the perimeter of a sector calculator depends on the known values of the sector’s radius (r), angle in radians (θ) or angle in degrees (α).

If the sector angle is given in radians, the formula for the perimeter of a sector is:

Perimeter = r × θ

If the sector angle is given in degrees, the formula for the perimeter of a sector is:

Perimeter = (α/360) × 2πr + 2r

Where, r = radius of the sector θ = angle of the sector in radians α = angle of the sector in degrees

Note that in the second formula, the first term ( (α/360) × 2πr) calculates the length of the arc of the sector, while the second term (2r) calculates the length of the two radii that make up the sector.

Example: Find the perimeter of a sector with a radius of 8 cm and a sector angle of 90 degrees.

Solution: Since the sector angle is given in degrees, we’ll use the second formula:

Perimeter = (α/360) × 2πr + 2r

We know that the radius of the sector is 8 cm and the sector angle is 90 degrees, so we can substitute these values into the formula:

Perimeter = (90/360) × 2π(8) + 2(8)

Perimeter = (0.25) × 2π(8) + 16

Perimeter = 4π + 16

Perimeter ≈ 28.85 cm

Therefore, the perimeter of the sector is approximately 28.85 cm.

## Frequently Asked Questions

Here are some of the mostly asked questions…

### What is a sector?

A sector is a portion of a circle bounded by two radii and an arc between them..

### What is the perimeter of a sector?

The perimeter of a sector is the total length of its boundary, which includes the arc and the two radii.

### How do you find the perimeter of a sector?

To find the perimeter of a sector, use the formula Perimeter = (θ/360) x 2πr + 2r, where θ is the angle of the sector in radians and r is the radius of the sector.

### What is the difference between a sector and a segment?

A sector is a portion of a circle bounded by two radii and an arc, while a segment is a portion of a circle bounded by a chord and an arc.

### What is the formula for the arc length of a sector?

The formula for the arc length of a sector is Arc Length = θr, where θ is the angle of the sector in radians and r is the radius of the sector.

### What is the formula for the area of a sector?

The formula for the area of a sector is A = (θ/2π) x πr^2, where θ is the angle of the sector in radians and r is the radius of the sector.

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