AP EAMCET · Maths · Application of Derivatives
The diameter and altitude of a right circular cone, at a certain instant, were found to be and respectively. If its diameter is increasing at a rate of , then at what rate must its altitude change, in order to keep its volume constant?
- A
- B
- C
- D
Answer & Solution
Correct Answer
(D)
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.
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