A sector is cut from a circle of radius 21 cm.

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Question:

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

 

Solution:

Given:
Radius = 2 cm

Angle of sector $=150^{\circ}$

Now,

Length of the arc $=\frac{2 \pi r \theta}{360}$

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

$=55 \mathrm{~cm}$

Area of the sector $=\frac{\pi r^{2} \theta}{360}$

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

$=577.5 \mathrm{~cm}$

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