Question

A sector is cut from a circle of radius 21 CM the angle of the sector is 150 degree find the length of Arc and area

Answer 1

Thank you for asking this question. Here is your answer:

r = 21 cm

Θ = 120°

The length of arc = 2πr x θ/360

= 2 x 22/7 x 21 x 120/360

= 44 cm

Area of Sector = πr² x θ/360

= 22 x 21 = 462cm²

If there is any confusion please leave a comment below.

Answer 2

Answer:

The length of arc is 55 cm

The area is 577.5 cm²

Step-by-step explanation:

Given,

radius = 21 cm

angle of sector = 150°

To find the length of Arc :

We know when angle is entire 360°, the length ( Circumference ) is 2πR

So,

when angle is θ, the length will be ( θ / 360 ) * 2πR

Here,

θ = 150°

R = 21 cm

Substituting the values in the formula,

Length of arc = $\frac{150}{360} * 2\pi *21$

= $\frac{150}{360} * 2 *\frac{22}{7} * 21$

= 55 cm

Similarly for Area:

We know when angle is entire 360°, the area is πR²

So,

when angle is θ, the length will be ( θ / 360 ) * πR²

Substituting the values,

Area = $\frac{150}{360} * \pi *21 *21$

= $\frac{150}{360} * \frac{22}{7} *21 *21$

= 577.5 cm²

Hence,

The length of arc is 55 cm

The area is 577.5 cm²