d The sector of a circle has radius of 21 cm and central angle

Mensuration MCQ2 (Sector of Circle, angle, perimeter)

Mensuration MCQ2 : The sector of a circle has radius of 21 cm and central angle 135 degree . Find its perimeter?

A. 91.5 cm          b) 93.5 cm                   c) 94.5 cm                      d) 92.5 cm



We know that perimeter is the length of the boundary of an area:

Here we are given following data;

Radius of the circle = R = 21 cm

drawit diagram 1

Central angle = ​\( \theta \)​= 135 deg

Perimeter of the sector covered by the angle \( \theta \) = ?

See the figure below;

The perimeter of the sector is’

\[ Perimeter=R+R+S \]

\[ =2R+S \]

We have value of R given as 21 cm but we will have to calculate value of arc length S using formula

\[ S=R\theta \]


\[ S= 21\times 135deg=21\times 135\times\frac{\pi}{180} \]

Note:Above we converted degree angle to radians — because above formula application requires angle in radians instead!

\[ S= 21\times 135\times\frac{3.14}{180}=49.455 cm \]

So putting values of R and S in above perimeter formula we get;

\[ Perimeter=2\times 21+49.455=91.455 cm \]

Hence perimeter of the sector is 91.455 cm or 91.5 cm approx.———– option  C is correct answer !


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