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

Sum

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

#### Solution

The arc length l and area A of a sector of angle θ in a circle of radius r are given by

l=\frac{\theta }{360}\times 2\pi r\text{ and A=}\frac{\theta}{360}\times \pi r^{2}\text{ respectively}\text{.}

Here, r = 21 cm and q = 150

\therefore \text{ }l={ \frac{150}{360}\times 2\times\frac{22}{7}\times 21}\text{cm}=\text{55 cm}

\text{and A}={ \frac{150}{360}\times \frac{22}{7}\times(21)^{2}}

= 577.5 cm2

Concept: Circumference of a Circle
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