Question

The perimeter of a sector of a circle of radius r cm and of central angle θ (in degrees) is .................
A. $2r\left( {\dfrac{{\pi \theta }}{{360}} + 2} \right)$
B. $2r\left( {\dfrac{{\pi \theta }}{{360}} + 1} \right)$
C. $2r\left( {\dfrac{{\pi \theta }}{{180}} + 1} \right)$
D. $2r\left( {\dfrac{{\pi \theta }}{{1800}} + 2} \right)$

Answer 1

Hint: In order to solve this problem we just need to use the formula arc length is equal to angle in radians multiplied by radius of the circle whose arc is a part.

Complete step-by-step answer:

We know that the length of the arc L = Angle in radians multiplied by radius of the circle whose arc is a part.

Angle subtended by the arc in radians is $\dfrac{{\pi \theta }}{{180}}$.

Using the formula $L = \theta \,{\text{x}}\,r$

L= $\dfrac{{\pi \theta }}{{180}}$r = $\dfrac{{2\pi \theta }}{{360}}$r …….(1)

So, the perimeter is $r + r + \dfrac{{2\pi \theta }}{{360}}r$= $2r\left( {\dfrac{{\pi \theta }}{{360}} + 1} \right)$.

Hence, the correct option is B.

Note: To solve this problem need to know the formula $L = \theta \,{\text{x}}\,r$ of length of arc and the conversion a degrees = $\dfrac{{\pi {\text{a}}}}{{180}}$ radians. We should also know that the formula of arc length is valid only when the angle is in radians. Then we found the perimeter, as the perimeter is nothing but the sum of all sides.