COMEDK · Maths · 27. Application of Derivatives
The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side three times as long as the other, is
- A Equal to shorter side of base
- B \(\dfrac{1}{2} \times\) shorter side of base
- C 3 times shorter side of base
- D \(\dfrac{3}{2} \times\) shorter side of base
Answer & Solution
Correct Answer
(D) \(\dfrac{3}{2} \times\) shorter side of base
Step-by-step Solution
Detailed explanation
Let the sides of the rectangular base be \(x\) and \(3x\). Let the height of the box be \(h\). The volume \(V\) of the box is given by \(V = (x)(3x)(h) = 3x^2 h\). Since \(V\) is fixed, \(h = \dfrac{V}{3x^2}\). The surface area \(S\) of the covered box is…
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