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TS EAMCET · Maths · Application of Derivatives

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is \(45^{\circ}\), then the approximate error in its volume is (in cu. cm)

  1. A \(1.078\)
  2. B \(3.08\)
  3. C \(1.54\)
  4. D \(6.16\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1.54\)

Step-by-step Solution

Detailed explanation

\(V = \frac{1}{3}\pi r^2 h\) \(r = D/2\), \(h = r/\tan\alpha = D/(2\tan\alpha)\) \(V = \frac{1}{3}\pi \left(\frac{D}{2}\right)^2 \left(\frac{D}{2\tan\alpha}\right) = \frac{\pi D^3}{24\tan\alpha}\) \(\frac{dV}{dD} = \frac{\pi (3D^2)}{24\tan\alpha} = \frac{\pi D^2}{8\tan\alpha}\)…