CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 2024 by Teachoo
This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.3
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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
