A sector is cut from a circle of radius 21 cm. The angle of the sector is 150∘. Find the length of its arc and area.

Radius of the circle is given as 21cm.
Area of sector,

A = \frac{θπ r^{2}}{360}

\Rightarrow A = \frac{150}{360} \times \frac{22}{7} \times 21 \times 21

\Rightarrow A = \frac{5}{12} \times 22 \times 3 \times 21

\Rightarrow A = 577.5 {cm}^{2}

Use formula

l = \frac{θπr}{180}

to calculate arc length,

l = \frac{θπr}{180}

\Rightarrow l = \frac{150}{180} \times \frac{22}{7} \times 21

\Rightarrow l = \frac{15}{18} \times 66

\Rightarrow l = 55 cm

Hence, area of sector is

577.5 {cm}^{2}

and arc length is

55 cm

.
Therefore, option 3 is correct.

A sector is cut from a circle of radius 21 cm. The angle of the sector is $150^{\circ}$ . Find the length of its arc and area.