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Question

A box is made from a piece of metal sheet 24cms square by cutting equal small squares from each corner and turning up the edges. If the volume of the box is maximum then the dimensions of the box are


A
16,16,4
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B
9, 9, 6
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C
8, 8, 8
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D
9, 9, 8
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Solution

The correct option is A 16,16,4
Let square of a cm edge is removed
So Length$$=$$breath$$=24-2a$$ of box
$$height = a$$
Volume $$=(24-2a)^2a$$
$$\frac {dv}{da}=(24-2a)^2-4(24-2a)a$$
$$0=(24-2a_)(24-6a)$$
$$a=12, 4$$
So Length$$=$$ breath$$=16$$
$$height =4$$

Applied Mathematics

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