Class 12 Applications Of Derivatives · Short Answer2 Marksrelated_rates
Class 12 Maths · Applications Of Derivatives · Short Answer #47
A cube volume increases at 9 cm³/s. Find the rate of increase of surface area when its edge is 10 cm.
✅ Step-by-Step Solution
Final Answer: 3.6 cm²/s
- For edge x, V=x³ and S=6x².
- V̇=3x²ẋ=9 gives ẋ=3/x². Thus Ṡ=12x ẋ=36/x.
- At x=10, Ṡ=3.6 cm²/s.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For edge x, V=x³ and S=6x².
- [1 mark] V̇=3x²ẋ=9 gives ẋ=3/x². Thus Ṡ=12x ẋ=36/x.
- [0.5 marks] At x=10, Ṡ=3.6 cm²/s.
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