NCERT Class 12 · Ch 6 Exercise 6.1 · Q14
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 14
Sand enters a conical heap at 12 cm³/s. Height is one-sixth of base radius. Find the height rate at h=4 cm.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: 1/(48π) cm/s.
- Since r=6h, V=(π/3)r²h=12πh³.
- Differentiate in time: Vₜ=36πh²hₜ. At h=4, 12=576πhₜ, so hₜ=1/(48π) cm/s.
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