**Problem 1 :**

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

**Problem 2 :**

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

**Problem 3 :**

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

**Problem 4 :**

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

**Problem 5 :**

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

**Problem 6 :**

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

**Problem 7 :**

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

**Problem 8 :**

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

**Problem 1 :**

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

**Solution :**

**Area of the sector = (θ/360**°**) **⋅** **π**r ^{2}**

**Substitute r = 42, ****θ = **60° and π** **≈** 22/7**

**≈**** (60**°**/360**°**)****(22/7)(42)**^{2}

= (1/6) ⋅ (22/7) ⋅ 42 ⋅ 42

= 924

So, the required area is about 924 cm^{2}

**Problem 2 :**

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

**Solution:**

**Area of the sector = (θ/360**°**) **⋅** **π**r ^{2}**

**Substitute r = 21, ****θ = **60° and π** **≈** 22/7**

**≈**** (60**°**/360**°**)****(22/7)(21)**^{2}

= (1/6) ⋅ (22/7) ⋅ 21 ⋅ 21

= 231

So, the required ares is about 231 cm^{2}.

**Problem 3 :**

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

**Solution :**

**Area of the sector = (θ/360**°**) **⋅** **π**r ^{2}**

**Substitute r = 4.9, ****θ = 3**0° and π** **≈** 22/7**

**≈**** (30**°**/360**°**)****(22/7)(4.9)**^{2}

= (1/12) ⋅ (22/7) ⋅ 4.9 ⋅ 4.9

**≈** 6.3

So, the required area is about 6.3 cm^{2}.

**Question 4 :**

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

**Solution :**

Area of the sector = (lr/2) square units

Substitute r = 6 and l = 20

= (20 ⋅ 6) / 2

= 60 cm^{2}

**Question 5 :**

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

**Solution :**

Diameter = 10 cm

Radius = Diameter / 2 = 10/2 = 5 cm

Area of the sector is

= (lr/2) square units

Substitute r = 5 and l = 40

= (40 ⋅ 5) / 2

= 100 cm^{2}

**Problem 6 :**

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

**Solution :**

Area of the sector = lr/2

Substitute r = 21 and l = 66.

= (66 x 21) / 2

= 693 cm^{2}

Using the area of the sector 693 cm^{2}, find the central angle θ.

Area of the sector = 693 cm^{2}

(θ/360°) ⋅ π**r ^{2}** = 693

**Substitute r = 21** and π** **≈** 22/7.**

(θ/360) ⋅ (22/7) ⋅ 21^{2} = 693

(θ/60°) ⋅ 231 = 693

θ = 693 ⋅ (60°/231)

θ = 180°

**Problem 7 :**

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

**Solution :**

Given : Radius is 35 cm and perimeter of the sector is 147 cm.

Perimeter of sector = 147 cm

l + 2r = 147

l + 2(35) = 147

l + 70 = 147

l = 77 cm

Area of the sector is

= (lr/2) square units

Substitute r = 35 and l = 77

= (77 ⋅ 35) / 2

= 2695/2

= 1347.5 cm^{2}

**Problem 8 :**

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

**Solution :**

Given : Radius is 20 cm and perimeter of the sector is 110 cm.

Perimeter of sector = 110 cm

l + 2r = 110

l + 2(20) = 110

l + 40 = 110

l = 70 cm

Area of the sector is

= (lr/2) square units

Substitute r = 20 and l = 70.

= (70 x 20) / 2

= 700 cm^{2}

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