# a sector of a circle of radius 8cm has an angle of 120 degrees at the centre find its perimeter and its area take pie as 3.142

## since 120° is 1/3 of a circle, it will have 1/3 the area, or

1/3 * πr^2

and since the arc length is 1/3 the circumference of the circle, the perimeter is 2r + 1/3 (2πr)

## Well, since you mentioned pie, I'm guessing you're hungry for some math humor! Let's dive in, shall we?

To find the perimeter of the sector, we need to calculate the length of the curved part of the sector, which is also known as the arc.

The arc length can be found using the formula:
arc length = (angle/360) x (2 x pi x radius)

So, putting in the values for your sector:
arc length = (120/360) x (2 x 3.142 x 8) = 2.095 cm (approximately)

Now, let's move on to the area of the sector. The formula for the area of the sector is:

area = (angle/360) x (pi x radius^2)

Plugging in the values:
area = (120/360) x (3.142 x 8^2) = 67.082 cm^2 (approximately)

So, the perimeter of the sector is approximately 2.095 cm, and the area is approximately 67.082 cm^2. Remember, these are just mathematical calculations - not delicious pies!

## To find the perimeter and the area of a sector of a circle, you need to use the formulas:

Perimeter of a Sector = (arc length) + (2 * radius)
Area of a Sector = (angle / 360) * (π * radius^2)

Let's calculate them step by step:

1. Perimeter of a Sector:
Given that the radius (r) is 8 cm, and the angle (θ) is 120 degrees, we need to find the arc length.

Arc Length = (angle / 360) * (2 * π * radius)
Arc Length = (120 / 360) * (2 * 3.142 * 8)

Calculating the arc length:
Arc Length = (1/3) * (2 * 3.142 * 8)
Arc Length = (2/3) * 3.142 * 8

Now we can calculate the perimeter:
Perimeter = (arc length) + (2 * radius)
Perimeter = (2/3) * 3.142 * 8 + (2 * 8)

Calculating the perimeter:
Perimeter = (2/3) * 3.142 * 8 + 16

2. Area of a Sector:
To find the area, we use the formula given above, replacing the values with the given measurements.

Area = (angle / 360) * (π * radius^2)
Area = (120 / 360) * (3.142 * 8^2)

Calculating the area:
Area = (1/3) * 3.142 * (8^2)
Area = (1/3) * 3.142 * 64

Now, let's calculate the perimeter and area:

Perimeter ≈ (2/3) * 3.142 * 8 + 16
Area ≈ (1/3) * 3.142 * 64