NCERT Class 12 · Ch 6 Exercise 6.1 · Q12
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 12
An air bubble radius increases at 1/2 cm/s. Find its volume rate at radius 1 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: 2π cm³/s.
- Vₜ=4πr²rₜ for a sphere.
- At r=1, rₜ=1/2, Vₜ=4π·1·1/2=2π cm³/s.
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