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CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q263 Marksrelated_rates

CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 26 (Applications Of Derivatives)

The volume of a cube increases at a constant rate k. Prove that its surface-area rate is inversely proportional to edge length s.

✅ Step-by-Step Solution

Final Answer: dA/dt=4k/s.
  1. Use V=s³ and A=6s².
  2. Differentiate to obtain k=3s² ds/dt and dA/dt=12s ds/dt.
  3. Substitute ds/dt=k/(3s²), giving 4k/s.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use V=s³ and A=6s².
  • [2 marks] Differentiate to obtain k=3s² ds/dt and dA/dt=12s ds/dt.
  • [0.5 marks] Substitute ds/dt=k/(3s²), giving 4k/s.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/5/3

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