NCERT Class 12 · Ch 6 Exercise 6.3 · Q21
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 21
For a closed cylindrical can of volume 100 cm³, find dimensions minimizing surface area.
💡 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: r=(50/π)^(1/3) cm; h=2(50/π)^(1/3) cm.
- The volume constraint gives h=100/(πr²), r>0. Surface area S=2πr²+2πrh=2πr²+200/r.
- S′=4πr−200/r²=0 gives r³=50/π.
- S″=4π+400/r³>0 and S tends to infinity at 0 and infinity, so this is the global minimum. The constraint then gives h=2r.
Master Chapter 6: Applications Of Derivatives
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
← Previous Question
Show that a right circular cylinder with fixed surface area and…
Next Question →Cut 28 m wire into a square perimeter and circle circumference to…
All Questions in Applications Of Derivatives — Exercise 6.3
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.