# Ex 6.5,18

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,18 A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ? Let m be the length of a side of the removed square Length after removing = 45 = 45 2 Breadth after removing = 24 = 24 2 Height of the box = We need to maximize volume of box Let V be the volume of a box Volume of a cuboid = l b h = 45 2 24 2 = 45 24 2 2 24 2 = 1080 90 48 +4 2 = 1080 90 2 48 2 +4 3 = 1080 138 2 +4 3 = 2 540 69 2 +2 3 = 2 2 3 69 2 +540 V = 2 2 3 69 2 +540 Diff w.r.t V = 2 2 3 69 2 + 540 = 2 6 2 69 2 +540 = 2 6 2 138 +540 = 2 6 2 23 +90 = 12 2 23 +90 Putting V =0 12 2 23 +90 =0 2 23 +90=0 2 5 18 +90=0 5 18 5 =0 18 5 =0 So, x = 18 & x = 5 If = 18 Breadth of a box = 24 2 = 24 2(18) = 24 36 = 12 Since, breadth cannot be negative, x = 18 is not possible Hence = 5 only Finding V V =12 2 23 +90 V =12 2 23 Putting =5 V 5 =12 2 5 23 = 12 10 23 = 12 13 = 156 V <0 when =5 Thus, V is maximum at =5 Square of side 5 cm is cut off from each Corner

Ex 6.3,5
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Ex 6.3,7 Important

Ex 6.3,12 Important

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Ex 6.3,26 Important

Example 35 Important

Example 37 Important

Example 38 Important

Example 40 Important

Ex 6.5,1 Important

Ex 6.5,5 Important

Ex 6.5,7 Important

Ex 6.5,11 Important

Ex 6.5,18 Important You are here

Ex 6.5,20 Important

Ex 6.5,23 Important

Ex 6.5,26 Important

Ex 6.5,28 Important

Example 46 Important

Example 47 Important

Misc 6 Important

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Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.