This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.3

Please check the question here 

https://www.teachoo.com/4427/712/Ex-6.5--18---A-rectangular-sheet-of-tin-45-cm-by-24-cm-is-made/category/Ex-6.5/

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Question 36 (Case Based Questions) Ramesh, the owner of a sweet selling shop, purchased some rectangular card board sheets of dimension 25 cm by 40 cm to make container packets without top. Let 𝒙 𝐜𝐦 be the length of the side of the square to be cut out from each comer to give that sheet the shape of the container by folding up the flaps.Let 𝑥 be the length of a side of the removed square Thus, Length after removing = 40 – 𝑥 –𝑥 = 40 – 2𝑥 Breadth after removing = 25 –𝑥 –𝑥 = 25 – 2𝑥 Height of the box = 𝑥 Question 36 (i) Express the volume (V) of each container as function of 𝒙 only.Let V be the volume of a box Volume of a cuboid = 𝑙 × 𝑏 × ℎ = (𝟒𝟎−𝟐𝒙)(𝟐𝟓−𝟐𝒙)(𝒙) = [40(25−2𝑥)−2𝑥(25−2𝑥)]𝑥 = (1000−80𝑥−50𝑥+4𝑥^2 )𝑥 =1000𝑥−80𝑥^2−50𝑥^2+4𝑥^3 = 1000𝑥−130𝑥^2+4𝑥^3 = 2(500𝑥−65𝑥^2+2𝑥^3 ) = 2(𝟐𝒙^𝟑−𝟔𝟓𝒙^𝟐+𝟓𝟎𝟎𝒙) cm3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.