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NCERT Class 12 · Ch 9 Exercise 9.3 · Q19

NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 19

A spherical balloon volume increases at a constant rate. Its radius is 3 initially and 6 after 3 s. Find radius at t seconds.

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: r(t)=(27+63t)^(1/3), t≥0.
  1. V=(4π/3)r³ and Vₜ is constant, so r³ is affine in t: r³=27+kt.
  2. At t=3, 216=27+3k, giving k=63. Take the positive cube root.

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