Mathbee CBSE Mathbee · CBSE Class 12 Maths
NCERT Class 12 · Ch 6 Exercise 6.3 · Q17

NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 17

Cut equal corner squares from a 18 cm × 18 cm tin sheet and fold an open box. Find the cut size maximizing volume.
Optimal box net: cut 3 cm squares
Optimal box net: cut 3 cm squares

💡 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: Cut side 3 cm; maximum volume 432 cm³.
  1. If cut side is x, the box has base (18−2x)×(18−2x), height x, and 0<x<9.0.
  2. V(x)=\(x \left(18 - 2 x\right)^{2}\); V′=\(12 \left(x - 9\right) \left(x - 3\right)\).
  3. The only stationary point in the feasible interval is x=3. The derivative changes from positive to negative there, while volume tends to zero at the feasible endpoints.
  4. Therefore the maximum volume is V(3)=432 cm³.

Master Chapter 6: Applications Of Derivatives

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Find positive numbers with sum 16 and minimum sum of cubes.
Next Question →
Cut equal corner squares from a 45 cm × 24 cm tin sheet and fold an…

All Questions in Applications Of Derivatives — Exercise 6.3

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29

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.