# HOW TO FIND RADIUS WHEN ARC LENGTH IS GIVEN

## About "How to find radius when arc length is given"

**How to find radius when arc length is given ?**

Here we are going to see some examples problems to show, how to find radius when arc length is given.

**Example 1 :**

The arc length of a sector is 66 cm and the central angle is 30°. Find its radius.

**Solution :**

Arc length of a sector = 66 cm

Central angle = 30°

** = (θ/360) **⋅ 2**Π**r

**66 = (30/360) **⋅ 2 ⋅ (22/7) ⋅ r

(66 ⋅ 7 ⋅ 360) / (30 ⋅ 22 ⋅ 2) = r

r = 126 cm

Hence the radius of the sector is 126 cm.

## How to find radius, central angle and perimeter of sector ?

**Example 2 :**

Find the radius, central angle and perimeter of a sector whose arc length and area are 27.5 cm and 618.75 cm^{2} respectively.

**Solution :**

Given that l = 27.5 cm and Area = 618.75 cm^{2}. So,

Area = lr/2

= 618.75 cm^{2}

(275 ⋅ r)/2 = 618.75

r = 45 cm

Hence, perimeter is l + 2r = 27.5 + 2(45) = 117.5cm

Now, arc length is given by (θ/360) ⋅ 2**Π**r = l

(θ/360) ⋅ 2 ⋅ (22/7) ⋅ 45 = 27.5

θ = 35°

## How to find radius when area and arc length is given ?

**Example 3 :**

Find the radius of the sector of area 225 cm^{2} and having an arc length of 15 cm

**Solution :**

Area of sector = 225 cm^{2 } ---(1)

Arc length = 15 cm

Area of sector = lr/2 ---(2)

(1) = (2)

225 = (15 ⋅ r)/2

(225 ⋅ 2)/15 = r

r = 30 cm

Hence the radius of sector is 30 cm.

**Example 4 :**

Find the radius, central angle and perimeter of a sector whose length of arc and area are 4.4 m and 9.24 m^{2} respectively

**Solution :**

Given that l = 4.4 m and Area = 9.24 m^{2}. So,

Area = lr/2

= 9.24 m^{2}

(4.4 ⋅ r)/2 = 9.24

r = (2 (9.24))/4.4

r = 4.2

Hence, perimeter is l + 2r = 4.4 + 2(4.2) = 12.8 m

Now, arc length is given by (θ/360) ⋅ 2**Π**r = l

(θ/360) ⋅ 2 ⋅ (22/7) ⋅ 4.2 = 4.4

θ = (4.4 ⋅ 7 ⋅ 360)/(2 ⋅ 22 ⋅ 4.2)

θ = 60°

Hence the required angle and radius are 60° and 4.2 m respectively.

After having gone through the stuff given above, we hope that the students would have understood "How to find radius when arc length is given".

Apart from the stuff given above, if you want to know more about "How to find radius when arc length is given".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.