**Question 1 :**

Find the length of arc whose radius is 42 cm and central angle is 60°.

**Question 2 :**

Find the length of arc whose radius is 10.5 cm and central angle is 36°.

**Question 3 :**

Find the length of arc whose radius is 21 cm and central angle is 120°.

**Question 4 :**

Find the length of an arc, if the radius of circle is 14 cm and area of the sector is 63 square cm.

**Question 5 :**

Find the length of arc, if the perimeter of a sector is 45 cm and radius is 10 cm.

**Question 6 :**

Find the arc length whose central angle is 180° and perimeter of circle is 64 cm.

**Question 7 :**

Find the area of the sector whose arc length is 20 cm and radius is 7 cm.

**Question 8 :**

A pendulum swings through an angle of 30° and describes an arc length of 11 cm. Find the length of the pendulum.

**Question 1 :**

Find the length of arc whose radius is 42 cm and central angle is 60°.

**Answer :**

Arc length is

= (θ/360°) ⋅ 2πr

Substitute r = 42 and θ = 60°.

= (60°/360°) ⋅ 2 ⋅ (22/7) ⋅ 42

= (1/4) ⋅ 2 ⋅ 22 ⋅ 6

= 66

So, the length of the arc is 11 cm.

**Question 2 :**

Find the length of arc whose radius is 10.5 cm and central angle is 36°.

**Answer :**

Arc length is

= (θ/360°) ⋅ 2πr

Substitute r = 10.5 and θ = 36°.

= (36°/360°) ⋅ 2 ⋅ (22/7) ⋅ 10.5

= (1/10) ⋅ 2 ⋅ 22 ⋅ 1.5

= 6.6

So, the length of the arc is 6.6 cm.

**Question 3 :**

Find the length of arc whose radius is 21 cm and central angle is 120°.

**Answer :**

Arc length is

= (θ/360°) ⋅ 2πr

Substitute r = 21 and θ = 120°.

= (120°/360°) ⋅ 2 ⋅ (22/7) ⋅ 21

= (1/3) ⋅ 2 ⋅ 22 ⋅ 3

= 44

So, the length of the arc is 44 cm.

**Question 4 :**

Find the length of an arc, if the radius of circle is 14 cm and area of the sector is 63 square cm.

**Answer :**

Area of the sector = 63 square cm

lr/2 = 63

Substitute r = 14 cm.

l(14)/2 = 63

l(7) = 63

l = 9 cm

So, the required arc length is 9 cm.

**Question 5 :**

Find the length of arc, if the perimeter of a sector is 45 cm and radius is 10 cm.

**Answer :**

Perimeter of sector = 45 cm

l + 2r = 45

Substitute r = 10 cm.

l + 2(10) = 45

l + 20 = 45

l = 45 - 20

l = 25 cm

**Question 6 :**

Find the arc length whose central angle is 180° and perimeter of circle is 64 cm.

**Answer :**

Perimeter of circle = 64 cm

That is,

2πr = 64

Arc length is

l = (θ/360**°**) ⋅ 2πr

Substitute θ = 180° and** **2πr = 64.

** **l = (180**°**/360**°**) ⋅ 64

l = (1/2) ⋅ 64

l = 32 cm

l = 32 cm

**Question 7 :**

Find the area of the sector whose arc length is 20 cm and radius is 7 cm.

**Answer :**

Area of sector = lr/2

Substitute l = 20 and r = 7.

Area of sector = (20 x 7) / 2

Area of sector = 70 square units.

**Question 8 :**

A pendulum swings through an angle of 30° and describes an arc length of 11 cm. Find the length of the pendulum.

**Answer :**

**Arc length of sector = 11 cm**

**sector angle = 30**°

If the pendulum swings once, then it forms a sector and the radius of the sector is the length of the pendulum.

So,

l = (θ/360°) x 2πr

Substitute the known values and solve for r.

11 = (30°/360°) x 2 x (22/7) x r

11 = (1/12) x 2 x (22/7) x r

r = (11 x 7 x 12)/(2 x 22)

r = 7 x 3

r = 21 cm

So, the length of pendulum is 21 cm.

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