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Class 12 Applications Of Derivatives · Short Answer2 Marksrelated_rates

Class 12 Maths · Applications Of Derivatives · Short Answer #40

Sand is poured at 12 cm³/s into a conical heap whose height is always one-sixth of its base radius. Find dh/dt when h=4 cm.

✅ Step-by-Step Solution

Final Answer: 1/(48π) cm/s
  1. r=6h, so V=πr²h/3=12πh³.
  2. Differentiate: 12=36πh² dh/dt, so dh/dt=1/(3πh²).
  3. At h=4, dh/dt=1/(48π) cm/s.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] r=6h, so V=πr²h/3=12πh³.
  • [1 mark] Differentiate: 12=36πh² dh/dt, so dh/dt=1/(3πh²).
  • [0.5 marks] At h=4, dh/dt=1/(48π) cm/s.

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