NCERT Class 12 · Ch 6 Miscellaneous Exercise · Q16
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Miscellaneous Exercise Question 16
A cylindrical tank of radius 10 m receives wheat at 314 m³/h. Find the depth rate.
💡 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: A: approximately 1 m/h (using π≈3.14); exact rate 3.14/π m/h.
- With fixed radius, V=100πh, so Vₜ=100πhₜ.
- Therefore hₜ=314/(100π)=3.14/π≈0.99949 m/h. Using the textbook approximation π=3.14 gives 1 m/h, option A.
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