A. 91.5 cm b) 93.5 cm c) 94.5 cm d) 92.5 cm
Mensuration MCQ2 (Sector of Circle, angle, perimeter)
Solution:
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
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
\[ S=R\theta \]
So,
\[ S= 21\times 135deg=21\times 135\times\frac{\pi}{180} \]
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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