Question

The length of arc of a sector of a circle of radius 14 cm is 10 cm. Find the area of the sector.​

Answer 1

Given:

✰ Radius of a circle = 14 cm

✰ The length of arc of a sector of a circle = 10 cm

To find:

✠ The area of the sector.

Solution:

We will find the area of a sector by using formula, but for that we need to find the angle theta or the central angle. To find that we will use the formula of length of arc. Putting the values in the formula and then doing the required calculations, we will find out the central angle and then the area of the sector.

Let's find out...✧

✭ Length of arc = 2πr × θ/360° ✭

Here,

• Central angle = θ
• Take value of π as 3.14

Putting the values in the formula, we have:

➛ 10 = 2 × 3.14 × 14 × θ/360

➛ θ = ( 360 × 10 )/( 3.14 × 2 × 14 )

➛ θ = 3600/87.92

➛ θ = 40.95°

Now,

✭ Area of sector = πr² × θ/360 ✭

➤ Area of sector = 3.14 × 14² × 40.95/360

➤ Area of sector = 3.14 × 196 × 40.95/360

➤ Area of sector = 615.44 × 40.95/360

➤ Area of sector = 70 cm²

∴ The area of the sector = 70 cm²

_______________________________