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AP EAMCET · Maths · Application of Derivatives

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?

  1. A 4 cm/s
  2. B 6 cm/s
  3. C -4 cm/s
  4. D -8 cm/s
Verified Solution

Answer & Solution

Correct Answer

(D) -8 cm/s

Step-by-step Solution

Detailed explanation

Let D is diameter, h is altitude and r is radius of the right circular cone. dDdt=2cm/s drdt=1cm/s V=13πr2h dVdt=13πdr2hdt dVdt=13πr2dhdt+2rdrdt×h 0=π325dhdt+10×20×1 0=25dhdt+200 dhdt=-8cm/s.