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AP EAMCET · Maths · Application of Derivatives

The perimeter of a sector is constant. If its area is to be maximum, the sectorical angle should be

  1. A \(\frac{\pi^c}{6}\)
  2. B \(\frac{\pi^c}{4}\)
  3. C \(4^C\)
  4. D \(2^c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2^c\)

Step-by-step Solution

Detailed explanation

Perimeter, \(P=2 r+r \theta=r(2+\theta)\) According to question, \(r(2+\theta)=k \Rightarrow r=\frac{k}{\theta+2}\) Let \(A\) be the area to the sector \(A=\frac{1}{2} r^2 \theta=\frac{k^2}{2} \cdot \frac{\theta}{(\theta+2)^2}\)…