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Class 12 Applications Of Derivatives · Mcq Single Correct1 Marksoptimization

Class 12 Maths · Applications Of Derivatives · Mcq Single Correct #15

A wire of length 20 cm forms the two radii and arc of a circular sector. Find the maximum enclosed area.

(A) 20 cm²
(B) 25 cm²
(C) 10 cm²
(D) 30 cm²

✅ Step-by-Step Solution

Final Answer: Option (B): 25 cm²

If the radius is r and arc length l=20−2r, then A=rl/2=10r−r²=25−(r−5)². Equality at r=5 is feasible (sector angle 2 radians).

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