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Class 10 › Mathematics › Areas Related to Circles
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
The perimeter of the shaded region in the given figure is : (In the figure, $O$ is the centre of the circle, two radii each of length $r$ are drawn to the circle, $a$ is the chord joining their end points and $l$ is the length of the corresponding arc. The shaded region is bounded by the two radii and the arc.)
A. $l$
B. $l+a$
C. $l+2r$
D. $l+2r+a$
✅ Answer & Solution
✅ Correct Answer: C
Step 1: Perimeter (boundary length) of a region is the total length of all curves and segments forming its outer boundary.
Step 2: The shaded region here is a sector. Its boundary consists of three parts: two radii and the arc.
Step 3: Add the boundary lengths.
$$\text{Perimeter}=r+r+l=l+2r$$
Step 4: The chord $a$ is inside the region, not a part of its outer boundary, so it is not counted.
Correct option is (C) $l+2r$.
