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AP EAMCET202120 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively. If its diameter is increasing at a rate of 2 cm / s , then at what rate must its altitude change, in order to keep its volume constant?

Options

  1. A4   cm / s
  2. B6   cm / s
  3. C- 4   cm / s
  4. D- 8   cm / s

Correct answer

D. - 8   cm / s

Step-by-step solution

Let D is diameter, h is altitude and r is radius of the right circular cone. d D d t = 2 cm / s d r d t = 1 cm / s V = 1 3 π r 2 h d V d t = 1 3 π d r 2 h d t d V d t = 1 3 π r 2 d h d t + 2 r d r d t × h 0 = π 3 25 d h d t + 10 × 20 × 1 0 = 25 d h d t + 200 d h d t = - 8 cm / s .

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