NCERT Class 12 · Ch 6 Exercise 6.1 · Q3
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 3
A circle radius increases at 3 cm/s. Find the area rate at radius 10 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: 60π cm²/s.
- A=πr², so dA/dt=2πr·dr/dt.
- At r=10 and rₜ=3, this is 2π·10·3=60π cm²/s.
Master Chapter 6: Applications Of Derivatives
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
← Previous Question
A cube volume increases at 8 cm³/s. Find the surface-area rate when…
Next Question →A cube edge increases at 3 cm/s. Find its volume rate at edge 10 cm.
All Questions in Applications Of Derivatives — Exercise 6.1
Related Questions in Applications Of Derivatives
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximal open interval on which f(x)=x²e^(−x) has positive derivative.
Class 12 Applications Of Derivatives · Mcq Single Correct
For f(x)=x²−4x+6, identify the maximal open interval where f′(x)>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
For x>0, at which x is f(x)=x^x stationary?
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum value of (1/x)^x for x>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum of [x(x−1)+1]^(1/3) on 0≤x≤1.
Class 12 Applications Of Derivatives · Mcq Single Correct
A trapezium area model is A(x)=(10+x)√(100−x²) cm² for 0≤x≤10. Find its maximum.