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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

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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.

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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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