Question

an open sided box is to made from a square cardboard with sides measuring 24cm, by cutting equal squares out of the corners and turning up the sides. find the height of the box that will give an maximum value

Answer 1

Answer:

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Answer 2

The height of the box will be 4 cm.

Step-by-step explanation:

If four squares with sides x cm are cut from the corners of the big square with sides 24 cm then, the volume of the open sided box will be given by,

V = x(24 - 2x)² = x(24² - 96x + 4x²) = 576x - 96x² + 4x³

⇒ $\frac{dV}{dx}$ = 576 - 192x + 12x² = 0 {Condition for maximum volume is $\frac{dV}{dx} = 0$}

⇒ x² - 16x + 48 = 0

⇒ x² - 12x - 4x + 48 = 0

⇒ (x - 12)(x - 4) = 0

Hence, x = 12 {Which is not possible} or x = 4.

Therefore, the height of the box will be 4 cm. (Answer)