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CUET · MATHS · PYQ PAPER 2025

A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is

  1. A 2856 \(cm ^3\)
  2. B 3256 \(cm ^3\)
  3. C 3656 \(cm ^3\)
  4. D 3456 \(cm ^3\)
Verified Solution

Answer & Solution

Correct Answer

(D) 3456 \(cm ^3\)

Step-by-step Solution

Detailed explanation

\(V(x) = (36 - 2x)^2 x = 4x^3 - 144x^2 + 1296x\) \(V'(x) = 12x^2 - 288x + 1296\) \(12x^2 - 288x + 1296 = 0 \implies x^2 - 24x + 108 = 0\) \((x - 6)(x - 18) = 0 \implies x = 6\) (since \(x \(V_{max} = (36 - 2(6))^2 (6)\) \(V_{max} = (24)^2 (6)\)…